Simplify (5^2)^-1

${(5^{2})}^{- 1}$

Step 1

Multiply the exponents in ${(5^{2})}^{- 1}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5^{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$5^{- 2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5^{2}}$

Step 3

Raise $5$ to the power of $2$ .

$\frac{1}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$