Simplify ((25c^-1)/5)^2

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

Step 1

Move $c^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{25}{5 c})}^{2}$

Step 2

Cancel the common factor of $25$ and $5$ .

Factor $5$ out of $25$ .

${(\frac{5 \cdot 5}{5 c})}^{2}$

Cancel the common factors.

Factor $5$ out of $5 c$ .

${(\frac{5 \cdot 5}{5 (c)})}^{2}$

Cancel the common factor.

${(\frac{5 \cdot 5}{5 c})}^{2}$

Rewrite the expression.

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

Step 3

Simplify the expression.

Apply the product rule to $\frac{5}{c}$ .

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

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

$\frac{25}{c^{2}}$