Precalculus Examples

${(3 x^{3} y^{- 4})}^{3}$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Move $3$ to the left of $x^{3}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{27 {(x^{3})}^{3}}{{(y^{4})}^{3}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{27 x^{3 \cdot 3}}{{(y^{4})}^{3}}$

Step 5.2.2

Multiply $3$ by $3$ .

$\frac{27 x^{9}}{{(y^{4})}^{3}}$

Step 6

Multiply the exponents in ${(y^{4})}^{3}$ .

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Step 6.1

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

$\frac{27 x^{9}}{y^{4 \cdot 3}}$

Step 6.2

Multiply $4$ by $3$ .

$\frac{27 x^{9}}{y^{12}}$