Simplify the Radical Expression cube root of (6b^2)/c

$\sqrt[3]{\frac{6 b^{2}}{c}}$

Step 1

Rewrite $\sqrt[3]{\frac{6 b^{2}}{c}}$ as $\frac{\sqrt[3]{6 b^{2}}}{\sqrt[3]{c}}$ .

$\frac{\sqrt[3]{6 b^{2}}}{\sqrt[3]{c}}$

Step 2

Multiply $\frac{\sqrt[3]{6 b^{2}}}{\sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

$\frac{\sqrt[3]{6 b^{2}}}{\sqrt[3]{c}} \cdot \frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{6 b^{2}}}{\sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{\sqrt[3]{c} {\sqrt[3]{c}}^{2}}$

Raise $\sqrt[3]{c}$ to the power of $1$ .

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{1} {\sqrt[3]{c}}^{2}}$

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

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{3}}$

Rewrite ${\sqrt[3]{c}}^{3}$ as $c$ .

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

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{{(c^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{c^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{c^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{c^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{c^{1}}$

Simplify.

$\frac{\sqrt[3]{6 b^{2}} {\sqrt[3]{c}}^{2}}{c}$

Step 4

Rewrite ${\sqrt[3]{c}}^{2}$ as ${(c^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{6 b^{2}} \sqrt[3]{c^{2}}}{c}$

Step 5

Combine using the product rule for radicals.

$\frac{\sqrt[3]{6 b^{2} c^{2}}}{c}$