Precalculus Examples

${(27 a^{3} b^{9})}^{\frac{1}{3}}$

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 $27 a^{3} b^{9}$ .

${(27 a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 1.2

Apply the product rule to $27 a^{3}$ .

$27^{\frac{1}{3}} {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{1}{3}} {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 2.2

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

$3^{3 (\frac{1}{3})} {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$3^{3 (\frac{1}{3})} {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 3.2

Rewrite the expression.

$3^{1} {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 4

Evaluate the exponent.

$3 {(a^{3})}^{\frac{1}{3}} {(b^{9})}^{\frac{1}{3}}$

Step 5

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

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Step 5.1

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

$3 a^{3 (\frac{1}{3})} {(b^{9})}^{\frac{1}{3}}$

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

Cancel the common factor.

$3 a^{3 (\frac{1}{3})} {(b^{9})}^{\frac{1}{3}}$

Step 5.2.2

Rewrite the expression.

$3 a^{1} {(b^{9})}^{\frac{1}{3}}$

Step 6

Simplify.

$3 a {(b^{9})}^{\frac{1}{3}}$

Step 7

Multiply the exponents in ${(b^{9})}^{\frac{1}{3}}$ .

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Step 7.1

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

$3 a b^{9 (\frac{1}{3})}$

Step 7.2

Cancel the common factor of $3$ .

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Step 7.2.1

Factor $3$ out of $9$ .

$3 a b^{3 (3) \frac{1}{3}}$

Step 7.2.2

Cancel the common factor.

$3 a b^{3 \cdot 3 \frac{1}{3}}$

Step 7.2.3

Rewrite the expression.

$3 a b^{3}$