Solve (10/10)^8*(10^-2/10^3)^8

$$( \frac { 10 } { 10 } ) ^ { 8 } \times ( \frac { 10 ^ { - 2 } } { 10 ^ { 3 } } ) ^ { 8 }$$

Evaluate

$$\frac{1}{10000000000000000000000000000000000000000}= 10^{-40}$$

Solution Steps

Divide 10 by 10 to get 1.

$$1^{8}\times \left(\frac{10^{-2}}{10^{3}}\right)^{8}$$

Rewrite 10^{3} as 10^{-2}\times 10^{5}. Cancel out 10^{-2} in both numerator and denominator.

$$1^{8}\times \left(\frac{1}{10^{5}}\right)^{8}$$

Calculate 1 to the power of 8 and get 1.

$$1\times \left(\frac{1}{10^{5}}\right)^{8}$$

Calculate 10 to the power of 5 and get 100000.

$$1\times \left(\frac{1}{100000}\right)^{8}$$

Calculate \frac{1}{100000} to the power of 8 and get \frac{1}{10000000000000000000000000000000000000000}.

$$1\times \frac{1}{10000000000000000000000000000000000000000}$$

Multiply 1 and \frac{1}{10000000000000000000000000000000000000000} to get \frac{1}{10000000000000000000000000000000000000000}.

$$\frac{1}{10000000000000000000000000000000000000000}$$

Factor

$$\frac{1}{2 ^ {40} \cdot 5 ^ {40}} = 1 \times 10^{-40}$$