Solve frac{4*8.99*10^{95}*(1.6*10^{-19})^{10}*9.1*110^{-31}}{(3*10^8)^3*(1.05*10^-34J*5)^6}

$$\frac { 4 \times 8.99 \times 10 ^ { 95 } \times ( 1.6 \times 10 ^ { - 19 } ) ^ { 10 } \times 9.1 \times 110 ^ { - 31 } } { ( 3 \times 10 ^ { 8 } ) ^ { 3 } \times ( 1.05 \times 10 ^ { - 34 } J \cdot 5 ) ^ { 6 } }$$

Evaluate

$$\frac{21053427538031594700800000000000000000000000000000000000000000}{63497223038883269309374796112004854349791J^{6}}$$

Solution Steps

Multiply 4 and 8.99 to get 35.96.

$$\frac{35.96\times 10^{95}\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of 95 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{35.96\times 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 35.96 and 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 1.6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate \frac{1}{6250000000000000000} to the power of 10 and get \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply \frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000} and 9.1 to get \frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 110 to the power of -31 and get \frac{1}{1919434249577504805041468412918110000000000000000000000000000000}.

$$\frac{\frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}\times \frac{1}{1919434249577504805041468412918110000000000000000000000000000000}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply \frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000} and \frac{1}{1919434249577504805041468412918110000000000000000000000000000000} to get \frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(3\times 100000000\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 3 and 100000000 to get 300000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{300000000^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 300000000 to the power of 3 and get 27000000000000000000000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(1.05\times \frac{1}{10000000000000000000000000000000000}J\times 5\right)^{6}}$$

Multiply 1.05 and \frac{1}{10000000000000000000000000000000000} to get \frac{21}{200000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{200000000000000000000000000000000000}J\times 5\right)^{6}}$$

Multiply \frac{21}{200000000000000000000000000000000000} and 5 to get \frac{21}{40000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{40000000000000000000000000000000000}J\right)^{6}}$$

Expand \left(\frac{21}{40000000000000000000000000000000000}J\right)^{6}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{40000000000000000000000000000000000}\right)^{6}J^{6}}$$

Calculate \frac{21}{40000000000000000000000000000000000} to the power of 6 and get \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Multiply 27000000000000000000000000 and \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Express \frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}} as a single fraction.

$$\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Multiply 436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{444480561272182885165623572784033980448537}{1801439850948198400000000000000000000000000000000000000000}.

$$\frac{81809}{\frac{444480561272182885165623572784033980448537}{1801439850948198400000000000000000000000000000000000000000}J^{6}}$$

Expand

$$\frac{21053427538031594700800000000000000000000000000000000000000000}{63497223038883269309374796112004854349791J^{6}}$$

Solution Steps

Multiply 4 and 8.99 to get 35.96.

$$\frac{35.96\times 10^{95}\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of 95 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{35.96\times 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 35.96 and 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 1.6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{10}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate \frac{1}{6250000000000000000} to the power of 10 and get \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 3596000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{1}{90949470177292823791503906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000}\times 9.1\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply \frac{899}{22737367544323205947875976562500000000000000000000000000000000000000000000000000000000000000000} and 9.1 to get \frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}\times 110^{-31}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 110 to the power of -31 and get \frac{1}{1919434249577504805041468412918110000000000000000000000000000000}.

$$\frac{\frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000}\times \frac{1}{1919434249577504805041468412918110000000000000000000000000000000}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply \frac{81809}{227373675443232059478759765625000000000000000000000000000000000000000000000000000000000000000000} and \frac{1}{1919434249577504805041468412918110000000000000000000000000000000} to get \frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(3\times 10^{8}\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(3\times 100000000\right)^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Multiply 3 and 100000000 to get 300000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{300000000^{3}\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 300000000 to the power of 3 and get 27000000000000000000000000.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(1.05\times 10^{-34}J\times 5\right)^{6}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(1.05\times \frac{1}{10000000000000000000000000000000000}J\times 5\right)^{6}}$$

Multiply 1.05 and \frac{1}{10000000000000000000000000000000000} to get \frac{21}{200000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{200000000000000000000000000000000000}J\times 5\right)^{6}}$$

Multiply \frac{21}{200000000000000000000000000000000000} and 5 to get \frac{21}{40000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{40000000000000000000000000000000000}J\right)^{6}}$$

Expand \left(\frac{21}{40000000000000000000000000000000000}J\right)^{6}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \left(\frac{21}{40000000000000000000000000000000000}\right)^{6}J^{6}}$$

Calculate \frac{21}{40000000000000000000000000000000000} to the power of 6 and get \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{27000000000000000000000000\times \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Multiply 27000000000000000000000000 and \frac{85766121}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Express \frac{\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}} as a single fraction.

$$\frac{81809}{436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}J^{6}}$$

Multiply 436428820098059260326742426722855725529370829463005065917968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{2315685267}{4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{444480561272182885165623572784033980448537}{1801439850948198400000000000000000000000000000000000000000}.

$$\frac{81809}{\frac{444480561272182885165623572784033980448537}{1801439850948198400000000000000000000000000000000000000000}J^{6}}$$