Solve (1/5)^7*(1/125)^2

$$( \frac { 1 } { 5 } ) ^ { 7 } \cdot ( \frac { 1 } { 125 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{1220703125}=8.192 \cdot 10^{-10}$$

Solution Steps

Calculate \frac{1}{5} to the power of 7 and get \frac{1}{78125}.

$$\frac{1}{78125}\times \left(\frac{1}{125}\right)^{2}$$

Calculate \frac{1}{125} to the power of 2 and get \frac{1}{15625}.

$$\frac{1}{78125}\times \frac{1}{15625}$$

Multiply \frac{1}{78125} times \frac{1}{15625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{78125\times 15625}$$

Do the multiplications in the fraction \frac{1\times 1}{78125\times 15625}.

$$\frac{1}{1220703125}$$

Factor

$$\frac{1}{5 ^ {13}} = 8.192 \times 10^{-10}$$