Precalculus Examples

${(\frac{1}{3} \cdot (x^{4} y^{- 3}))}^{- 2}$

Step 1

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

${(\frac{1}{3} \cdot (x^{4} \frac{1}{y^{3}}))}^{- 2}$

Step 2

Combine $x^{4}$ and $\frac{1}{y^{3}}$ .

${(\frac{1}{3} \cdot \frac{x^{4}}{y^{3}})}^{- 2}$

Step 3

Combine.

${(\frac{1 x^{4}}{3 y^{3}})}^{- 2}$

Step 4

Multiply $x^{4}$ by $1$ .

${(\frac{x^{4}}{3 y^{3}})}^{- 2}$

Step 5

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

${(\frac{3 y^{3}}{x^{4}})}^{2}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{3 y^{3}}{x^{4}}$ .

$\frac{{(3 y^{3})}^{2}}{{(x^{4})}^{2}}$

Step 6.2

Apply the product rule to $3 y^{3}$ .

$\frac{3^{2} {(y^{3})}^{2}}{{(x^{4})}^{2}}$

Step 7

Simplify the numerator.

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Step 7.1

Raise $3$ to the power of $2$ .

$\frac{9 {(y^{3})}^{2}}{{(x^{4})}^{2}}$

Step 7.2

Multiply the exponents in ${(y^{3})}^{2}$ .

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Step 7.2.1

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

$\frac{9 y^{3 \cdot 2}}{{(x^{4})}^{2}}$

Step 7.2.2

Multiply $3$ by $2$ .

$\frac{9 y^{6}}{{(x^{4})}^{2}}$

Step 8

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

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Step 8.1

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

$\frac{9 y^{6}}{x^{4 \cdot 2}}$

Step 8.2

Multiply $4$ by $2$ .

$\frac{9 y^{6}}{x^{8}}$