Algebra Examples

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

Step 1

Multiply ${(2 x)}^{\frac{1}{3}}$ by ${(2 x)}^{\frac{4}{3}}$ 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.

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $1$ and $4$ .

${(2 x)}^{\frac{5}{3}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{{(2 x)}^{5}}$