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

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

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

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

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

${(2 y^{2} x)}^{5}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 y^{2} x$ .

${(2 y^{2})}^{5} x^{5}$

Apply the product rule to $2 y^{2}$ .

$2^{5} {(y^{2})}^{5} x^{5}$

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

$32 {(y^{2})}^{5} x^{5}$

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

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

$32 y^{2 \cdot 5} x^{5}$

Multiply $2$ by $5$ .

$32 y^{10} x^{5}$