Algebra Examples

$27^{\frac{1}{3}} \cdot 27^{\frac{4}{3}}$

Step 1

Multiply $27^{\frac{1}{3}}$ by $27^{\frac{4}{3}}$ by adding the exponents.

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Step 1.1

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

$27^{\frac{1}{3} + \frac{4}{3}}$

Step 1.2

Combine the numerators over the common denominator.

$27^{\frac{1 + 4}{3}}$

Step 1.3

Add $1$ and $4$ .

$27^{\frac{5}{3}}$

Step 2

Simplify the expression.

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Step 2.1

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

${(3^{3})}^{\frac{5}{3}}$

Step 2.2

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

$3^{3 (\frac{5}{3})}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$3^{3 (\frac{5}{3})}$

Step 3.2

Rewrite the expression.

$3^{5}$

Step 4

Raise $3$ to the power of $5$ .

$243$