Precalculus Examples

${(8 x^{4} y^{6} z)}^{\frac{1}{3}}$

Step 1

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

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Step 1.1

Apply the product rule to $8 x^{4} y^{6} z$ .

${(8 x^{4} y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 1.2

Apply the product rule to $8 x^{4} y^{6}$ .

${(8 x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 1.3

Apply the product rule to $8 x^{4}$ .

$8^{\frac{1}{3}} {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{\frac{1}{3}} {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 2.2

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

$2^{3 (\frac{1}{3})} {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$2^{3 (\frac{1}{3})} {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 3.2

Rewrite the expression.

$2^{1} {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 4

Evaluate the exponent.

$2 {(x^{4})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 5

Multiply the exponents in ${(x^{4})}^{\frac{1}{3}}$ .

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Step 5.1

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

$2 x^{4 (\frac{1}{3})} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 5.2

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

$2 x^{\frac{4}{3}} {(y^{6})}^{\frac{1}{3}} z^{\frac{1}{3}}$

Step 6

Multiply the exponents in ${(y^{6})}^{\frac{1}{3}}$ .

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Step 6.1

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

$2 x^{\frac{4}{3}} y^{6 (\frac{1}{3})} z^{\frac{1}{3}}$

Step 6.2

Cancel the common factor of $3$ .

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Step 6.2.1

Factor $3$ out of $6$ .

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

Step 6.2.2

Cancel the common factor.

$2 x^{\frac{4}{3}} y^{3 \cdot 2 \frac{1}{3}} z^{\frac{1}{3}}$

Step 6.2.3

Rewrite the expression.

$2 x^{\frac{4}{3}} y^{2} z^{\frac{1}{3}}$

Step 7

Reorder factors in $2 x^{\frac{4}{3}} y^{2} z^{\frac{1}{3}}$ .

$2 y^{2} x^{\frac{4}{3}} z^{\frac{1}{3}}$