Algebra Examples

$\sqrt[3]{a}$

Step 1

Multiply to rationalize the numerator.

$\frac{\sqrt[3]{a} {\sqrt[3]{a}}^{2}}{{\sqrt[3]{a}}^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $\sqrt[3]{a}$ to the power of $1$ .

$\frac{{\sqrt[3]{a}}^{1} {\sqrt[3]{a}}^{2}}{{\sqrt[3]{a}}^{2}}$

Step 2.2

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

$\frac{{\sqrt[3]{a}}^{1 + 2}}{{\sqrt[3]{a}}^{2}}$

Step 2.3

Add $1$ and $2$ .

$\frac{{\sqrt[3]{a}}^{3}}{{\sqrt[3]{a}}^{2}}$

Step 2.4

Rewrite ${\sqrt[3]{a}}^{3}$ as $a$ .

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Step 2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{a}$ as $a^{\frac{1}{3}}$ .

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

Step 2.4.2

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

$\frac{a^{\frac{1}{3} \cdot 3}}{{\sqrt[3]{a}}^{2}}$

Step 2.4.3

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

$\frac{a^{\frac{3}{3}}}{{\sqrt[3]{a}}^{2}}$

Step 2.4.4

Cancel the common factor of $3$ .

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Step 2.4.4.1

Cancel the common factor.

$\frac{a^{\frac{3}{3}}}{{\sqrt[3]{a}}^{2}}$

Step 2.4.4.2

Rewrite the expression.

$\frac{a^{1}}{{\sqrt[3]{a}}^{2}}$

Step 2.4.5

Simplify.

$\frac{a}{{\sqrt[3]{a}}^{2}}$

Step 3

Rewrite ${\sqrt[3]{a}}^{2}$ as $\sqrt[3]{a^{2}}$ .

$\frac{a}{\sqrt[3]{a^{2}}}$