Solve [(5^-2:5^-5)^-2]^-1

$$[ ( 5 ^ { - 2 } : 5 ^ { - 5 } ) ^ { - 2 } ] ^ { - 1 }$$

Evaluate

$$15625$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -5 from -2 to get 3.

$$\left(\left(5^{3}\right)^{-2}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\left(5^{-6}\right)^{-1}$$

Calculate 5 to the power of -6 and get \frac{1}{15625}.

$$\left(\frac{1}{15625}\right)^{-1}$$

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

$$15625$$

Factor

$$5^{6}$$