Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite ${\sqrt[4]{5 x}}^{5}$ as $\sqrt[4]{{(5 x)}^{5}}$ .

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

Step 1.2

Apply the product rule to $5 x$ .

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

Step 1.3

Raise $5$ to the power of $5$ .

$\frac{1}{\sqrt[4]{3125 x^{5}}}$

Step 1.4

Rewrite $3125 x^{5}$ as ${(5 x)}^{4} \cdot (5 x)$ .

Tap for more steps...

Step 1.4.1

Factor $625$ out of $3125$ .

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

Step 1.4.2

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

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

Step 1.4.3

Factor out $x^{4}$ .

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

Step 1.4.4

Move $5$ .

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

Step 1.4.5

Rewrite $5^{4} x^{4}$ as ${(5 x)}^{4}$ .

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

Step 1.4.6

Add parentheses.

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Remove non-negative terms from the absolute value.

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

Step 2

Multiply $\frac{1}{5 | x | \sqrt[4]{5 x}}$ by $\frac{{\sqrt[4]{5 x}}^{3}}{{\sqrt[4]{5 x}}^{3}}$ .

$\frac{1}{5 | x | \sqrt[4]{5 x}} \cdot \frac{{\sqrt[4]{5 x}}^{3}}{{\sqrt[4]{5 x}}^{3}}$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{1}{5 | x | \sqrt[4]{5 x}}$ by $\frac{{\sqrt[4]{5 x}}^{3}}{{\sqrt[4]{5 x}}^{3}}$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | \sqrt[4]{5 x} {\sqrt[4]{5 x}}^{3}}$

Step 3.2

Move $\sqrt[4]{5 x}$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | (\sqrt[4]{5 x} {\sqrt[4]{5 x}}^{3})}$

Step 3.3

Raise $\sqrt[4]{5 x}$ to the power of $1$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | ({\sqrt[4]{5 x}}^{1} {\sqrt[4]{5 x}}^{3})}$

Step 3.4

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

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {\sqrt[4]{5 x}}^{1 + 3}}$

Step 3.5

Add $1$ and $3$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {\sqrt[4]{5 x}}^{4}}$

Step 3.6

Rewrite ${\sqrt[4]{5 x}}^{4}$ as $5 x$ .

Tap for more steps...

Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{5 x}$ as ${(5 x)}^{\frac{1}{4}}$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {({(5 x)}^{\frac{1}{4}})}^{4}}$

Step 3.6.2

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

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {(5 x)}^{\frac{1}{4} \cdot 4}}$

Step 3.6.3

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

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {(5 x)}^{\frac{4}{4}}}$

Step 3.6.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.6.4.1

Cancel the common factor.

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {(5 x)}^{\frac{4}{4}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | {(5 x)}^{1}}$

Step 3.6.5

Simplify.

$\frac{{\sqrt[4]{5 x}}^{3}}{5 | x | (5 x)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite ${\sqrt[4]{5 x}}^{3}$ as $\sqrt[4]{{(5 x)}^{3}}$ .

$\frac{\sqrt[4]{{(5 x)}^{3}}}{5 | x | (5 x)}$

Step 4.2

Apply the product rule to $5 x$ .

$\frac{\sqrt[4]{5^{3} x^{3}}}{5 | x | (5 x)}$

Step 4.3

Raise $5$ to the power of $3$ .

$\frac{\sqrt[4]{125 x^{3}}}{5 | x | (5 x)}$

Step 5

Multiply $5$ by $5$ .

$\frac{\sqrt[4]{125 x^{3}}}{25 | x | x}$

Step 6

Reorder factors in $\frac{\sqrt[4]{125 x^{3}}}{25 | x | x}$ .

$\frac{\sqrt[4]{125 x^{3}}}{25 x | x |}$