Finite Math Examples

$\sqrt[4]{\frac{x}{625}} \sqrt[4]{\frac{625}{y}}$

Step 1

Rewrite $\frac{x}{625}$ as ${(\frac{1}{5})}^{4} x$ .

Tap for more steps...

Step 1.1

Factor the perfect power $1^{4}$ out of $x$ .

$\sqrt[4]{\frac{1^{4} x}{625}} \sqrt[4]{\frac{625}{y}}$

Step 1.2

Factor the perfect power $5^{4}$ out of $625$ .

$\sqrt[4]{\frac{1^{4} x}{5^{4} \cdot 1}} \sqrt[4]{\frac{625}{y}}$

Step 1.3

Rearrange the fraction $\frac{1^{4} x}{5^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{5})}^{4} x} \sqrt[4]{\frac{625}{y}}$

Step 2

Pull terms out from under the radical.

$\frac{1}{5} \sqrt[4]{x} \sqrt[4]{\frac{625}{y}}$

Step 3

Combine $\frac{1}{5}$ and $\sqrt[4]{x}$ .

$\frac{\sqrt[4]{x}}{5} \sqrt[4]{\frac{625}{y}}$

Step 4

Rewrite $\sqrt[4]{\frac{625}{y}}$ as $\frac{\sqrt[4]{625}}{\sqrt[4]{y}}$ .

$\frac{\sqrt[4]{x}}{5} \cdot \frac{\sqrt[4]{625}}{\sqrt[4]{y}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Rewrite $625$ as $5^{4}$ .

$\frac{\sqrt[4]{x}}{5} \cdot \frac{\sqrt[4]{5^{4}}}{\sqrt[4]{y}}$

Step 5.2

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

$\frac{\sqrt[4]{x}}{5} \cdot \frac{5}{\sqrt[4]{y}}$

Step 6

Simplify terms.

Tap for more steps...

Step 6.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.1.1

Cancel the common factor.

$\frac{\sqrt[4]{x}}{5} \cdot \frac{5}{\sqrt[4]{y}}$

Step 6.1.2

Rewrite the expression.

$\sqrt[4]{x} \frac{1}{\sqrt[4]{y}}$

Step 6.2

Combine $\sqrt[4]{x}$ and $\frac{1}{\sqrt[4]{y}}$ .

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

Step 7

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

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

Step 8

Combine and simplify the denominator.

Tap for more steps...

Step 8.1

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

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

Step 8.2

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

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

Step 8.3

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

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

Step 8.4

Add $1$ and $3$ .

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

Step 8.5

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

Tap for more steps...

Step 8.5.1

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

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

Step 8.5.2

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

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

Step 8.5.3

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

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

Step 8.5.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 8.5.4.1

Cancel the common factor.

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

Step 8.5.4.2

Rewrite the expression.

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

Step 8.5.5

Simplify.

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

Step 9

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

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

Step 10

Combine using the product rule for radicals.

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