Algebra Examples

$\sqrt[4]{y^{\frac{7}{3}} y^{\frac{1}{3}}}$

Step 1

Multiply $y^{\frac{7}{3}}$ by $y^{\frac{1}{3}}$ 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.

$\sqrt[4]{y^{\frac{7}{3} + \frac{1}{3}}}$

Step 1.2

Combine the numerators over the common denominator.

$\sqrt[4]{y^{\frac{7 + 1}{3}}}$

Step 1.3

Add $7$ and $1$ .

$\sqrt[4]{y^{\frac{8}{3}}}$

Step 2

Rewrite $y^{\frac{8}{3}}$ as ${(y^{\frac{2}{3}})}^{4}$ .

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

Step 3

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

$y^{\frac{2}{3}}$