Precalculus Examples

${(\frac{5 x^{2}}{y^{- 2}})}^{- 4}$

Step 1

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(5 x^{2} y^{2})}^{- 4}$

Step 2

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

$\frac{1}{{(5 x^{2} y^{2})}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $5 x^{2} y^{2}$ .

$\frac{1}{{(5 x^{2})}^{4} {(y^{2})}^{4}}$

Step 3.2

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

$\frac{1}{5^{4} {(x^{2})}^{4} {(y^{2})}^{4}}$

Step 3.3

Raise $5$ to the power of $4$ .

$\frac{1}{625 {(x^{2})}^{4} {(y^{2})}^{4}}$

Step 3.4

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 3.4.1

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

$\frac{1}{625 x^{2 \cdot 4} {(y^{2})}^{4}}$

Step 3.4.2

Multiply $2$ by $4$ .

$\frac{1}{625 x^{8} {(y^{2})}^{4}}$

Step 3.5

Multiply the exponents in ${(y^{2})}^{4}$ .

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Step 3.5.1

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

$\frac{1}{625 x^{8} y^{2 \cdot 4}}$

Step 3.5.2

Multiply $2$ by $4$ .

$\frac{1}{625 x^{8} y^{8}}$