Basic Math Examples

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

Step 1

Combine $\sqrt[4]{a^{3} y^{2}}$ and $\sqrt[4]{a y^{3}}$ into a single radical.

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

Step 2

Reduce the expression $\frac{a^{3} y^{2}}{a y^{3}}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $a$ out of $a^{3} y^{2}$ .

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

Step 2.2

Factor $a$ out of $a y^{3}$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $y^{2}$ and $y^{3}$ .

Tap for more steps...

Step 3.1

Factor $y^{2}$ out of $a^{2} y^{2}$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $y^{2}$ out of $y^{3}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Rewrite $\sqrt[4]{\frac{a^{2}}{y}}$ as $\frac{\sqrt[4]{a^{2}}}{\sqrt[4]{y}}$ .

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Rewrite $\sqrt[4]{a^{2}}$ as $\sqrt{\sqrt{a^{2}}}$ .

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

Step 5.2

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

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

Step 6

Multiply $\frac{\sqrt{a}}{\sqrt[4]{y}}$ by $\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{3}}$ .

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

Step 7

Combine and simplify the denominator.

Tap for more steps...

Step 7.1

Multiply $\frac{\sqrt{a}}{\sqrt[4]{y}}$ by $\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{3}}$ .

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

Step 7.2

Raise $\sqrt[4]{y}$ to the power of $1$ .

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

Step 7.3

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

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

Step 7.4

Add $1$ and $3$ .

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

Step 7.5

Rewrite ${\sqrt[4]{y}}^{4}$ as $y$ .

Tap for more steps...

Step 7.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y}$ as $y^{\frac{1}{4}}$ .

$\frac{\sqrt{a} {\sqrt[4]{y}}^{3}}{{(y^{\frac{1}{4}})}^{4}}$

Step 7.5.2

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

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

Step 7.5.3

Combine $\frac{1}{4}$ and $4$ .

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

Step 7.5.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 7.5.4.1

Cancel the common factor.

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

Step 7.5.4.2

Rewrite the expression.

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

Step 7.5.5

Simplify.

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

Step 8

Rewrite ${\sqrt[4]{y}}^{3}$ as $\sqrt[4]{y^{3}}$ .

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

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Rewrite the expression using the least common index of $4$ .

Tap for more steps...

Step 9.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} \sqrt[4]{y^{3}}}{y}$

Step 9.1.2

Rewrite $a^{\frac{1}{2}}$ as $a^{\frac{2}{4}}$ .

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

Step 9.1.3

Rewrite $a^{\frac{2}{4}}$ as $\sqrt[4]{a^{2}}$ .

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

Step 9.2

Combine using the product rule for radicals.

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