Simplify (8 square root of 3)/( square root of k)

$\frac{8 \sqrt{3}}{\sqrt{k}}$

Step 1

Multiply $\frac{8 \sqrt{3}}{\sqrt{k}}$ by $\frac{\sqrt{k}}{\sqrt{k}}$ .

$\frac{8 \sqrt{3}}{\sqrt{k}} \cdot \frac{\sqrt{k}}{\sqrt{k}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{8 \sqrt{3}}{\sqrt{k}}$ by $\frac{\sqrt{k}}{\sqrt{k}}$ .

$\frac{8 \sqrt{3} \sqrt{k}}{\sqrt{k} \sqrt{k}}$

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

$\frac{8 \sqrt{3} \sqrt{k}}{{\sqrt{k}}^{1} \sqrt{k}}$

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

$\frac{8 \sqrt{3} \sqrt{k}}{{\sqrt{k}}^{1} {\sqrt{k}}^{1}}$

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

$\frac{8 \sqrt{3} \sqrt{k}}{{\sqrt{k}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{8 \sqrt{3} \sqrt{k}}{{\sqrt{k}}^{2}}$

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

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

$\frac{8 \sqrt{3} \sqrt{k}}{{(k^{\frac{1}{2}})}^{2}}$

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

$\frac{8 \sqrt{3} \sqrt{k}}{k^{\frac{1}{2} \cdot 2}}$

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

$\frac{8 \sqrt{3} \sqrt{k}}{k^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8 \sqrt{3} \sqrt{k}}{k^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{8 \sqrt{3} \sqrt{k}}{k^{1}}$

Simplify.

$\frac{8 \sqrt{3} \sqrt{k}}{k}$

Step 3

Combine using the product rule for radicals.

$\frac{8 \sqrt{k \cdot 3}}{k}$

Step 4

Move $3$ to the left of $k$ .

$\frac{8 \sqrt{3 k}}{k}$