Evaluate (y^(-1/2))^4

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

Step 1

Multiply the exponents in ${(y^{- \frac{1}{2}})}^{4}$ .

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

$y^{- \frac{1}{2} \cdot 4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y^{\frac{- 1}{2} \cdot 4}$

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y^{- 1 \cdot 2}$

Multiply $- 1$ by $2$ .

$y^{- 2}$

Step 2

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

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