Simplify 3/( sixth root of 2x^4)

$\frac{3}{\sqrt[6]{2 x^{4}}}$

Step 1

Multiply $\frac{3}{\sqrt[6]{2 x^{4}}}$ by $\frac{{\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{5}}$ .

$\frac{3}{\sqrt[6]{2 x^{4}}} \cdot \frac{{\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{5}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{3}{\sqrt[6]{2 x^{4}}}$ by $\frac{{\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{5}}$ .

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{\sqrt[6]{2 x^{4}} {\sqrt[6]{2 x^{4}}}^{5}}$

Raise $\sqrt[6]{2 x^{4}}$ to the power of $1$ .

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{1} {\sqrt[6]{2 x^{4}}}^{5}}$

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

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{1 + 5}}$

Add $1$ and $5$ .

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{\sqrt[6]{2 x^{4}}}^{6}}$

Rewrite ${\sqrt[6]{2 x^{4}}}^{6}$ as $2 x^{4}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{2 x^{4}}$ as ${(2 x^{4})}^{\frac{1}{6}}$ .

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{({(2 x^{4})}^{\frac{1}{6}})}^{6}}$

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

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{(2 x^{4})}^{\frac{1}{6} \cdot 6}}$

Combine $\frac{1}{6}$ and $6$ .

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{(2 x^{4})}^{\frac{6}{6}}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{(2 x^{4})}^{\frac{6}{6}}}$

Rewrite the expression.

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{{(2 x^{4})}^{1}}$

Simplify.

$\frac{3 {\sqrt[6]{2 x^{4}}}^{5}}{2 x^{4}}$

Step 3

Simplify the numerator.

Rewrite ${\sqrt[6]{2 x^{4}}}^{5}$ as ${({(2 x^{4})}^{5})}^{\frac{1}{6}}$ .

$\frac{3 \sqrt[6]{{(2 x^{4})}^{5}}}{2 x^{4}}$

Apply the product rule to $2 x^{4}$ .

$\frac{3 \sqrt[6]{2^{5} {(x^{4})}^{5}}}{2 x^{4}}$

Raise $2$ to the power of $5$ .

$\frac{3 \sqrt[6]{32 {(x^{4})}^{5}}}{2 x^{4}}$

Multiply the exponents in ${(x^{4})}^{5}$ .

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

$\frac{3 \sqrt[6]{32 x^{4 \cdot 5}}}{2 x^{4}}$

Multiply $4$ by $5$ .

$\frac{3 \sqrt[6]{32 x^{20}}}{2 x^{4}}$

Rewrite $32 x^{20}$ as ${(x^{3})}^{6} \cdot (32 x^{2})$ .

Factor out $x^{18}$ .

$\frac{3 \sqrt[6]{32 (x^{18} x^{2})}}{2 x^{4}}$

Rewrite $x^{18}$ as ${(x^{3})}^{6}$ .

$\frac{3 \sqrt[6]{32 ({(x^{3})}^{6} x^{2})}}{2 x^{4}}$

Reorder $32$ and ${(x^{3})}^{6}$ .

$\frac{3 \sqrt[6]{{(x^{3})}^{6} \cdot 32 x^{2}}}{2 x^{4}}$

Add parentheses.

$\frac{3 \sqrt[6]{{(x^{3})}^{6} \cdot (32 x^{2})}}{2 x^{4}}$

Pull terms out from under the radical.

$\frac{3 x^{3} \sqrt[6]{32 x^{2}}}{2 x^{4}}$

Step 4

Cancel the common factor of $x^{3}$ and $x^{4}$ .

Factor $x^{3}$ out of $3 x^{3} \sqrt[6]{32 x^{2}}$ .

$\frac{x^{3} (3 \sqrt[6]{32 x^{2}})}{2 x^{4}}$

Cancel the common factors.

Factor $x^{3}$ out of $2 x^{4}$ .

$\frac{x^{3} (3 \sqrt[6]{32 x^{2}})}{x^{3} (2 x)}$

Cancel the common factor.

$\frac{x^{3} (3 \sqrt[6]{32 x^{2}})}{x^{3} (2 x)}$

Rewrite the expression.

$\frac{3 \sqrt[6]{32 x^{2}}}{2 x}$

Simplify 3/( sixth root of 2x^4)

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