Precalculus Examples

${(- (216 t^{9}))}^{\frac{1}{3}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply $216$ by $- 1$ .

${(- 216 t^{9})}^{\frac{1}{3}}$

Step 1.2

Apply the product rule to $- 216 t^{9}$ .

${(- 216)}^{\frac{1}{3}} {(t^{9})}^{\frac{1}{3}}$

Step 1.3

Rewrite $- 216$ as ${(- 6)}^{3}$ .

${({(- 6)}^{3})}^{\frac{1}{3}} {(t^{9})}^{\frac{1}{3}}$

Step 1.4

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

${(- 6)}^{3 (\frac{1}{3})} {(t^{9})}^{\frac{1}{3}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

${(- 6)}^{3 (\frac{1}{3})} {(t^{9})}^{\frac{1}{3}}$

Step 2.2

Rewrite the expression.

${(- 6)}^{1} {(t^{9})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Evaluate the exponent.

$- 6 {(t^{9})}^{\frac{1}{3}}$

Step 3.2

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

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Step 3.2.1

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

$- 6 t^{9 (\frac{1}{3})}$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Factor $3$ out of $9$ .

$- 6 t^{3 (3) \frac{1}{3}}$

Step 3.2.2.2

Cancel the common factor.

$- 6 t^{3 \cdot 3 \frac{1}{3}}$

Step 3.2.2.3

Rewrite the expression.

$- 6 t^{3}$