Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

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

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

Step 1.2.2

Factor $2$ out of $4$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

$y^{- 1 \cdot 2}$

Step 1.3

Multiply $- 1$ by $2$ .

$y^{- 2}$

Step 2

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

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