Algebra Examples

$\sqrt[3]{\frac{y^{2}}{y^{\frac{4}{5}}}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move $y^{\frac{4}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\sqrt[3]{y^{2} y^{- \frac{4}{5}}}$

Step 1.2

Multiply $y^{2}$ by $y^{- \frac{4}{5}}$ by adding the exponents.

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Step 1.2.1

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

$\sqrt[3]{y^{2 - \frac{4}{5}}}$

Step 1.2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\sqrt[3]{y^{2 \cdot \frac{5}{5} - \frac{4}{5}}}$

Step 1.2.3

Combine $2$ and $\frac{5}{5}$ .

$\sqrt[3]{y^{\frac{2 \cdot 5}{5} - \frac{4}{5}}}$

Step 1.2.4

Combine the numerators over the common denominator.

$\sqrt[3]{y^{\frac{2 \cdot 5 - 4}{5}}}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $2$ by $5$ .

$\sqrt[3]{y^{\frac{10 - 4}{5}}}$

Step 1.2.5.2

Subtract $4$ from $10$ .

$\sqrt[3]{y^{\frac{6}{5}}}$

Step 2

Rewrite $y^{\frac{6}{5}}$ as ${(y^{\frac{2}{5}})}^{3}$ .

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

Step 3

Pull terms out from under the radical, assuming real numbers.

$y^{\frac{2}{5}}$