Solve (10^4)^2/(10^3)^5

$$\frac { ( 10 ^ { 4 } ) ^ { 2 } } { ( 10 ^ { 3 } ) ^ { 5 } }$$

Evaluate

$$\frac{1}{10000000}=0.0000001$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{10^{8}}{\left(10^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{10^{8}}{10^{15}}$$

Rewrite 10^{15} as 10^{8}\times 10^{7}. Cancel out 10^{8} in both numerator and denominator.

$$\frac{1}{10^{7}}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{1}{10000000}$$

Factor

$$\frac{1}{2 ^ {7} \cdot 5 ^ {7}} = 1 \times 10^{-7}$$