Algebra Examples

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

Step 1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $4$ and $2$ .

${(x^{\frac{6}{3}})}^{\frac{1}{3}}$

Step 1.4

Divide $6$ by $3$ .

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

Step 2

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

$\sqrt[3]{{(x^{2})}^{1}}$

Step 3

Anything raised to $1$ is the base itself.

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Step 3.1

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

$\sqrt[3]{x^{\frac{4}{3} + \frac{2}{3}}}$

Step 3.2

Combine the numerators over the common denominator.

$\sqrt[3]{x^{\frac{4 + 2}{3}}}$

Step 3.3

Add $4$ and $2$ .

$\sqrt[3]{x^{\frac{6}{3}}}$

Step 3.4

Divide $6$ by $3$ .

$\sqrt[3]{x^{2}}$