Solve frac{(1.6*10^{-19})^2*(0.15)^2*(1.5)^2}{2*1.6*10^-2z}

$$\frac { ( 1.6 \times 10 ^ { - 19 } ) ^ { 2 } \times ( 0.15 ) ^ { 2 } \times ( 1.5 ) ^ { 2 } } { 2 \times 1.6 \times 10 ^ { - 2 } z }$$

Evaluate

$$\frac{81}{2000000000000000000000000000000000000000z}$$

Solution Steps

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

$$\frac{\left(1.6\times \frac{1}{10000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

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

$$\frac{\left(\frac{1}{6250000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate \frac{1}{6250000000000000000} to the power of 2 and get \frac{1}{39062500000000000000000000000000000000}.

$$\frac{\frac{1}{39062500000000000000000000000000000000}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate 0.15 to the power of 2 and get 0.0225.

$$\frac{\frac{1}{39062500000000000000000000000000000000}\times 0.0225\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Multiply \frac{1}{39062500000000000000000000000000000000} and 0.0225 to get \frac{9}{15625000000000000000000000000000000000000}.

$$\frac{\frac{9}{15625000000000000000000000000000000000000}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$\frac{\frac{9}{15625000000000000000000000000000000000000}\times 2.25}{2\times 1.6\times 10^{-2}z}$$

Multiply \frac{9}{15625000000000000000000000000000000000000} and 2.25 to get \frac{81}{62500000000000000000000000000000000000000}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{2\times 1.6\times 10^{-2}z}$$

Multiply 2 and 1.6 to get 3.2.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{3.2\times 10^{-2}z}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{3.2\times \frac{1}{100}z}$$

Multiply 3.2 and \frac{1}{100} to get \frac{4}{125}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{\frac{4}{125}z}$$

Express \frac{\frac{81}{62500000000000000000000000000000000000000}}{\frac{4}{125}z} as a single fraction.

$$\frac{81}{62500000000000000000000000000000000000000\times \frac{4}{125}z}$$

Multiply 62500000000000000000000000000000000000000 and \frac{4}{125} to get 2000000000000000000000000000000000000000.

$$\frac{81}{2000000000000000000000000000000000000000z}$$

Expand

$$\frac{81}{2000000000000000000000000000000000000000z}$$

Solution Steps

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

$$\frac{\left(1.6\times \frac{1}{10000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

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

$$\frac{\left(\frac{1}{6250000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate \frac{1}{6250000000000000000} to the power of 2 and get \frac{1}{39062500000000000000000000000000000000}.

$$\frac{\frac{1}{39062500000000000000000000000000000000}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate 0.15 to the power of 2 and get 0.0225.

$$\frac{\frac{1}{39062500000000000000000000000000000000}\times 0.0225\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Multiply \frac{1}{39062500000000000000000000000000000000} and 0.0225 to get \frac{9}{15625000000000000000000000000000000000000}.

$$\frac{\frac{9}{15625000000000000000000000000000000000000}\times 1.5^{2}}{2\times 1.6\times 10^{-2}z}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$\frac{\frac{9}{15625000000000000000000000000000000000000}\times 2.25}{2\times 1.6\times 10^{-2}z}$$

Multiply \frac{9}{15625000000000000000000000000000000000000} and 2.25 to get \frac{81}{62500000000000000000000000000000000000000}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{2\times 1.6\times 10^{-2}z}$$

Multiply 2 and 1.6 to get 3.2.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{3.2\times 10^{-2}z}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{3.2\times \frac{1}{100}z}$$

Multiply 3.2 and \frac{1}{100} to get \frac{4}{125}.

$$\frac{\frac{81}{62500000000000000000000000000000000000000}}{\frac{4}{125}z}$$

Express \frac{\frac{81}{62500000000000000000000000000000000000000}}{\frac{4}{125}z} as a single fraction.

$$\frac{81}{62500000000000000000000000000000000000000\times \frac{4}{125}z}$$

Multiply 62500000000000000000000000000000000000000 and \frac{4}{125} to get 2000000000000000000000000000000000000000.

$$\frac{81}{2000000000000000000000000000000000000000z}$$