Simplify 1/(( fourth root of 5x)^5)

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

Simplify the denominator.

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

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

Apply the product rule to $5 x$ .

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

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

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

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

Factor $625$ out of $3125$ .

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

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

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

Factor out $x^{4}$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{{\sqrt[4]{5 x}}^{3}}{5 x^{2} \cdot 5}$

Simplify the numerator.

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

$\frac{\sqrt[4]{{(5 x)}^{3}}}{5 x^{2} \cdot 5}$

Apply the product rule to $5 x$ .

$\frac{\sqrt[4]{5^{3} x^{3}}}{5 x^{2} \cdot 5}$

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

$\frac{\sqrt[4]{125 x^{3}}}{5 x^{2} \cdot 5}$

Multiply $5$ by $5$ .

$\frac{\sqrt[4]{125 x^{3}}}{25 x^{2}}$

Simplify 1/(( fourth root of 5x)^5)

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