Precalculus Examples

${(\frac{- 8 x^{3}}{y^{- 6}})}^{\frac{2}{3}}$

Step 1

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(- 8 x^{3} y^{6})}^{\frac{2}{3}}$

Step 2

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

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Step 2.1

Apply the product rule to $- 8 x^{3} y^{6}$ .

${(- 8 x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 2.2

Apply the product rule to $- 8 x^{3}$ .

${(- 8)}^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Rewrite $- 8$ as ${(- 2)}^{3}$ .

${({(- 2)}^{3})}^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 3.2

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

${(- 2)}^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

${(- 2)}^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 4.2

Rewrite the expression.

${(- 2)}^{2} {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 5

Simplify the expression.

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Step 5.1

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

$4 {(x^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 5.2

Multiply the exponents in ${(x^{3})}^{\frac{2}{3}}$ .

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Step 5.2.1

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

$4 x^{3 (\frac{2}{3})} {(y^{6})}^{\frac{2}{3}}$

Step 5.2.2

Cancel the common factor of $3$ .

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Step 5.2.2.1

Cancel the common factor.

$4 x^{3 (\frac{2}{3})} {(y^{6})}^{\frac{2}{3}}$

Step 5.2.2.2

Rewrite the expression.

$4 x^{2} {(y^{6})}^{\frac{2}{3}}$

Step 5.3

Multiply the exponents in ${(y^{6})}^{\frac{2}{3}}$ .

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Step 5.3.1

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

$4 x^{2} y^{6 (\frac{2}{3})}$

Step 5.3.2

Cancel the common factor of $3$ .

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Step 5.3.2.1

Factor $3$ out of $6$ .

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

Step 5.3.2.2

Cancel the common factor.

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

Step 5.3.2.3

Rewrite the expression.

$4 x^{2} y^{2 \cdot 2}$

Step 5.3.3

Multiply $2$ by $2$ .

$4 x^{2} y^{4}$