Algebra Examples

${(- 27)}^{\frac{2}{3}} (81^{\frac{1}{4}})$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $- 27$ as ${(- 3)}^{3}$ .

${({(- 3)}^{3})}^{\frac{2}{3}} \cdot 81^{\frac{1}{4}}$

Step 1.2

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

${(- 3)}^{3 (\frac{2}{3})} \cdot 81^{\frac{1}{4}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

${(- 3)}^{3 (\frac{2}{3})} \cdot 81^{\frac{1}{4}}$

Step 2.2

Rewrite the expression.

${(- 3)}^{2} \cdot 81^{\frac{1}{4}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $- 3$ to the power of $2$ .

$9 \cdot 81^{\frac{1}{4}}$

Step 3.2

Rewrite $81$ as $3^{4}$ .

$9 \cdot {(3^{4})}^{\frac{1}{4}}$

Step 3.3

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

$9 \cdot 3^{4 (\frac{1}{4})}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$9 \cdot 3^{4 (\frac{1}{4})}$

Step 4.2

Rewrite the expression.

$9 \cdot 3^{1}$

Step 5

Evaluate the exponent.

$9 \cdot 3$

Step 6

Multiply $9$ by $3$ .

$27$