Simplify (4x^-2)^(-1/2)

${(4 x^{- 2})}^{- \frac{1}{2}}$

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

${(4 \frac{1}{x^{2}})}^{- \frac{1}{2}}$

Combine $4$ and $\frac{1}{x^{2}}$ .

${(\frac{4}{x^{2}})}^{- \frac{1}{2}}$

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

${(\frac{x^{2}}{4})}^{\frac{1}{2}}$

Apply the product rule to $\frac{x^{2}}{4}$ .

$\frac{{(x^{2})}^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Simplify the numerator.

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

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

$\frac{x^{2 (\frac{1}{2})}}{4^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{2 (\frac{1}{2})}}{4^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{x^{1}}{4^{\frac{1}{2}}}$

Simplify.

$\frac{x}{4^{\frac{1}{2}}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{x}{2}$