Simplify (5x^(-1/2))^-2

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

Step 1

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

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

Step 2

Combine $5$ and $\frac{1}{x^{\frac{1}{2}}}$ .

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

Apply the product rule to $\frac{x^{\frac{1}{2}}}{5}$ .

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

Step 5

Simplify the numerator.

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 6

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

$\frac{x}{25}$