Simplify -3/( fifth root of x^6)

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

Step 1

Simplify the denominator.

Factor out $x^{5}$ .

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

Pull terms out from under the radical.

$\frac{- 3}{x \sqrt[5]{x}}$

Step 2

Move the negative in front of the fraction.

$- \frac{3}{x \sqrt[5]{x}}$

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $4$ .

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

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

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

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

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

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

Combine $\frac{1}{5}$ and $5$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 5

Multiply $x$ by $x$ .

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

Step 6

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

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