Evaluate 5(25)^(-1/2)

$5 {(25)}^{- \frac{1}{2}}$

Step 1

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

$5 \frac{1}{25^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$5 (\frac{1}{5})$

Step 3

Cancel the common factor of $5$ .

Cancel the common factor.

$5 (\frac{1}{5})$

Rewrite the expression.

$1$