Solve 410^-54pileft(6.410^6right)^3/4pi10^-7

$$\frac{ 4 { 10 }^{ -5 } 4 \pi { \left(6.4 { 10 }^{ 6 } \right) }^{ 3 } }{ 4 \pi { 10 }^{ -7 } }$$

Evaluate

$$104857600000000000000000$$

Solution Steps

Cancel out 4\pi in both numerator and denominator.

$$\frac{4\times 10^{-5}\times \left(6.4\times 10^{6}\right)^{3}}{10^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4\times 10^{2}\times \left(6.4\times 10^{6}\right)^{3}$$

Calculate 10 to the power of 2 and get 100.

$$4\times 100\times \left(6.4\times 10^{6}\right)^{3}$$

Multiply 4 and 100 to get 400.

$$400\times \left(6.4\times 10^{6}\right)^{3}$$

Calculate 10 to the power of 6 and get 1000000.

$$400\times \left(6.4\times 1000000\right)^{3}$$

Multiply 6.4 and 1000000 to get 6400000.

$$400\times 6400000^{3}$$

Calculate 6400000 to the power of 3 and get 262144000000000000000.

$$400\times 262144000000000000000$$

Multiply 400 and 262144000000000000000 to get 104857600000000000000000.

$$104857600000000000000000$$

Factor

$$2^{37}\times 5^{17}$$