Pre-Algebra Examples

$\frac{\sqrt[4]{a^{5} b^{5}}}{a b}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $a^{5} b^{5}$ as ${(a b)}^{4} (a b)$ .

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Step 1.1.1

Factor out $a^{4}$ .

$\frac{\sqrt[4]{a^{4} a b^{5}}}{a b}$

Step 1.1.2

Factor out $b^{4}$ .

$\frac{\sqrt[4]{a^{4} a (b^{4} b)}}{a b}$

Step 1.1.3

Move $a$ .

$\frac{\sqrt[4]{a^{4} b^{4} a b}}{a b}$

Step 1.1.4

Rewrite $a^{4} b^{4}$ as ${(a b)}^{4}$ .

$\frac{\sqrt[4]{{(a b)}^{4} a b}}{a b}$

Step 1.1.5

Add parentheses.

$\frac{\sqrt[4]{{(a b)}^{4} (a b)}}{a b}$

$\frac{\sqrt[4]{{(a b)}^{4} (a b)}}{a b}$

Step 1.2

Pull terms out from under the radical.

$\frac{a b \sqrt[4]{a b}}{a b}$

$\frac{a b \sqrt[4]{a b}}{a b}$

Step 2

Cancel the common factor of $a$ .

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Step 2.1

Cancel the common factor.

$\frac{a b \sqrt[4]{a b}}{a b}$

Step 2.2

Rewrite the expression.

$\frac{b \sqrt[4]{a b}}{b}$

$\frac{b \sqrt[4]{a b}}{b}$

Step 3

Cancel the common factor of $b$ .

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Step 3.1

Cancel the common factor.

$\frac{b \sqrt[4]{a b}}{b}$

Step 3.2

Divide $\sqrt[4]{a b}$ by $1$ .

$\sqrt[4]{a b}$

$\sqrt[4]{a b}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$