Algebra Examples

$9^{\frac{1}{3}} \cdot 81^{\frac{1}{3}}$

Step 1

Multiply $9^{\frac{1}{3}} \cdot 81^{\frac{1}{3}}$ .

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Step 1.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.2

Multiply the exponents in ${(3^{2})}^{\frac{1}{3}}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine $2$ and $\frac{1}{3}$ .

$3^{\frac{2}{3}} \cdot 81^{\frac{1}{3}}$

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3^{\frac{2}{3} + \frac{4}{3}}$

Step 1.6

Combine the numerators over the common denominator.

$3^{\frac{2 + 4}{3}}$

Step 1.7

Add $2$ and $4$ .

$3^{\frac{6}{3}}$

Step 1.8

Cancel the common factor of $6$ and $3$ .

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Step 1.8.1

Factor $3$ out of $6$ .

$3^{\frac{3 \cdot 2}{3}}$

Step 1.8.2

Cancel the common factors.

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Step 1.8.2.1

Factor $3$ out of $3$ .

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

Step 1.8.2.2

Cancel the common factor.

$3^{\frac{3 \cdot 2}{3 \cdot 1}}$

Step 1.8.2.3

Rewrite the expression.

$3^{\frac{2}{1}}$

Step 1.8.2.4

Divide $2$ by $1$ .

$3^{2}$

Step 2

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

$9$