Simplify 10/( square root of 15x)

$\frac{10}{\sqrt{15 x}}$

Step 1

Multiply $\frac{10}{\sqrt{15 x}}$ by $\frac{\sqrt{15 x}}{\sqrt{15 x}}$ .

$\frac{10}{\sqrt{15 x}} \cdot \frac{\sqrt{15 x}}{\sqrt{15 x}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{10}{\sqrt{15 x}}$ by $\frac{\sqrt{15 x}}{\sqrt{15 x}}$ .

$\frac{10 \sqrt{15 x}}{\sqrt{15 x} \sqrt{15 x}}$

Raise $\sqrt{15 x}$ to the power of $1$ .

$\frac{10 \sqrt{15 x}}{{\sqrt{15 x}}^{1} \sqrt{15 x}}$

Raise $\sqrt{15 x}$ to the power of $1$ .

$\frac{10 \sqrt{15 x}}{{\sqrt{15 x}}^{1} {\sqrt{15 x}}^{1}}$

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

$\frac{10 \sqrt{15 x}}{{\sqrt{15 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{10 \sqrt{15 x}}{{\sqrt{15 x}}^{2}}$

Rewrite ${\sqrt{15 x}}^{2}$ as $15 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 x}$ as ${(15 x)}^{\frac{1}{2}}$ .

$\frac{10 \sqrt{15 x}}{{({(15 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{10 \sqrt{15 x}}{{(15 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{10 \sqrt{15 x}}{{(15 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{10 \sqrt{15 x}}{{(15 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{10 \sqrt{15 x}}{{(15 x)}^{1}}$

Simplify.

$\frac{10 \sqrt{15 x}}{15 x}$

Step 3

Cancel the common factor of $10$ and $15$ .

Factor $5$ out of $10 \sqrt{15 x}$ .

$\frac{5 (2 \sqrt{15 x})}{15 x}$

Cancel the common factors.

Factor $5$ out of $15 x$ .

$\frac{5 (2 \sqrt{15 x})}{5 (3 x)}$

Cancel the common factor.

$\frac{5 (2 \sqrt{15 x})}{5 (3 x)}$

Rewrite the expression.

$\frac{2 \sqrt{15 x}}{3 x}$