Solve 66*10^-34*3*10^8/66*10^-34*3*10^8/290*{10^-9}+15*16*{10}^-19

$$\frac{ \frac{ 66 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } }{ 66 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } } }{ 290 \times { 10 }^{ -9 } } +15 \times 16 \times { 10 }^{ -19 }$$

Evaluate

$$\frac{12500000000000000000000087}{3625000000000000000}\approx 3448275.862068966$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{\frac{66\times 10^{-26}\times 3}{66\times 10^{-34}\times 3\times 10^{8}}}{290\times 10^{-9}}+15\times 16\times 10^{-19}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{\frac{66\times 10^{-26}\times 3}{66\times 10^{-26}\times 3}}{290\times 10^{-9}}+15\times 16\times 10^{-19}$$

Divide 66\times 10^{-26}\times 3 by 66\times 10^{-26}\times 3 to get 1.

$$\frac{1}{290\times 10^{-9}}+15\times 16\times 10^{-19}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{1}{290\times \frac{1}{1000000000}}+15\times 16\times 10^{-19}$$

Multiply 290 and \frac{1}{1000000000} to get \frac{29}{100000000}.

$$\frac{1}{\frac{29}{100000000}}+15\times 16\times 10^{-19}$$

Divide 1 by \frac{29}{100000000} by multiplying 1 by the reciprocal of \frac{29}{100000000}.

$$1\times \frac{100000000}{29}+15\times 16\times 10^{-19}$$

Multiply 1 and \frac{100000000}{29} to get \frac{100000000}{29}.

$$\frac{100000000}{29}+15\times 16\times 10^{-19}$$

Multiply 15 and 16 to get 240.

$$\frac{100000000}{29}+240\times 10^{-19}$$

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

$$\frac{100000000}{29}+240\times \frac{1}{10000000000000000000}$$

Multiply 240 and \frac{1}{10000000000000000000} to get \frac{3}{125000000000000000}.

$$\frac{100000000}{29}+\frac{3}{125000000000000000}$$

Add \frac{100000000}{29} and \frac{3}{125000000000000000} to get \frac{12500000000000000000000087}{3625000000000000000}.

$$\frac{12500000000000000000000087}{3625000000000000000}$$

Factor

$$\frac{115849 \cdot 107899075520720938463}{2 ^ {15} \cdot 5 ^ {18} \cdot 29} = 3448275\frac{3.125000000595591 \times 10^{18}}{3.625 \times 10^{18}} = 3448275.8620689656$$