Simplify 10/( square root of 3x^5)

$\frac{10}{\sqrt{3 x^{5}}}$

Step 1

Simplify the denominator.

Rewrite $3 x^{5}$ as ${(x^{2})}^{2} \cdot (3 x)$ .

Factor out $x^{4}$ .

$\frac{10}{\sqrt{3 (x^{4} x)}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{10}{\sqrt{3 ({(x^{2})}^{2} x)}}$

Reorder $3$ and ${(x^{2})}^{2}$ .

$\frac{10}{\sqrt{{(x^{2})}^{2} \cdot 3 x}}$

Add parentheses.

$\frac{10}{\sqrt{{(x^{2})}^{2} \cdot (3 x)}}$

Pull terms out from under the radical.

$\frac{10}{x^{2} \sqrt{3 x}}$

Step 2

Multiply $\frac{10}{x^{2} \sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

$\frac{10}{x^{2} \sqrt{3 x}} \cdot \frac{\sqrt{3 x}}{\sqrt{3 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{10}{x^{2} \sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

$\frac{10 \sqrt{3 x}}{x^{2} \sqrt{3 x} \sqrt{3 x}}$

Move $\sqrt{3 x}$ .

$\frac{10 \sqrt{3 x}}{x^{2} (\sqrt{3 x} \sqrt{3 x})}$

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{10 \sqrt{3 x}}{x^{2} ({\sqrt{3 x}}^{1} \sqrt{3 x})}$

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{10 \sqrt{3 x}}{x^{2} ({\sqrt{3 x}}^{1} {\sqrt{3 x}}^{1})}$

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

$\frac{10 \sqrt{3 x}}{x^{2} {\sqrt{3 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{10 \sqrt{3 x}}{x^{2} {\sqrt{3 x}}^{2}}$

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

$\frac{10 \sqrt{3 x}}{x^{2} {({(3 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{10 \sqrt{3 x}}{x^{2} {(3 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{10 \sqrt{3 x}}{x^{2} {(3 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{10 \sqrt{3 x}}{x^{2} {(3 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{10 \sqrt{3 x}}{x^{2} {(3 x)}^{1}}$

Simplify.

$\frac{10 \sqrt{3 x}}{x^{2} (3 x)}$

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{10 \sqrt{3 x}}{x \cdot x^{2} \cdot 3}$

Multiply $x$ by $x^{2}$ .

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

$\frac{10 \sqrt{3 x}}{x^{1} x^{2} \cdot 3}$

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

$\frac{10 \sqrt{3 x}}{x^{1 + 2} \cdot 3}$

Add $1$ and $2$ .

$\frac{10 \sqrt{3 x}}{x^{3} \cdot 3}$

Step 5

Move $3$ to the left of $x^{3}$ .

$\frac{10 \sqrt{3 x}}{3 x^{3}}$

Simplify 10/( square root of 3x^5)

Related Questions

Support LCMGCF.com by disabling your adblocker.