Simplify (-8x^4)/( square root of x)

$\frac{- 8 x^{4}}{\sqrt{x}}$

Step 1

Move the negative in front of the fraction.

$- \frac{(8) x^{4}}{\sqrt{x}}$

Step 2

Multiply $\frac{8 x^{4}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$- (\frac{8 x^{4}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}})$

Step 3

Combine and simplify the denominator.

Multiply $\frac{8 x^{4}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$- \frac{8 x^{4} \sqrt{x}}{\sqrt{x} \sqrt{x}}$

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

$- \frac{8 x^{4} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

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

$- \frac{8 x^{4} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

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

$- \frac{8 x^{4} \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

$- \frac{8 x^{4} \sqrt{x}}{{\sqrt{x}}^{2}}$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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

$- \frac{8 x^{4} \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}}$

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

$- \frac{8 x^{4} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$- \frac{8 x^{4} \sqrt{x}}{x^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{8 x^{4} \sqrt{x}}{x^{\frac{2}{2}}}$

Rewrite the expression.

$- \frac{8 x^{4} \sqrt{x}}{x^{1}}$

Simplify.

$- \frac{8 x^{4} \sqrt{x}}{x}$

Step 4

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

Factor $x$ out of $8 x^{4} \sqrt{x}$ .

$- \frac{x (8 x^{3} \sqrt{x})}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$- \frac{x (8 x^{3} \sqrt{x})}{x^{1}}$

Factor $x$ out of $x^{1}$ .

$- \frac{x (8 x^{3} \sqrt{x})}{x \cdot 1}$

Cancel the common factor.

$- \frac{x (8 x^{3} \sqrt{x})}{x \cdot 1}$

Rewrite the expression.

$- \frac{8 x^{3} \sqrt{x}}{1}$

Divide $8 x^{3} \sqrt{x}$ by $1$ .

$- (8 x^{3} \sqrt{x})$

Step 5

Multiply $8$ by $- 1$ .

$- 8 x^{3} \sqrt{x}$

Simplify (-8x^4)/( square root of x)

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