Simplify the Radical Expression cube root of (27a^4)/(8b^3)

$\sqrt[3]{\frac{27 a^{4}}{8 b^{3}}}$

Step 1

Rewrite $\frac{27 a^{4}}{8 b^{3}}$ as ${(\frac{3 a}{2 b})}^{3} a$ .

Factor the perfect power ${(3 a)}^{3}$ out of $27 a^{4}$ .

$\sqrt[3]{\frac{{(3 a)}^{3} a}{8 b^{3}}}$

Factor the perfect power ${(2 b)}^{3}$ out of $8 b^{3}$ .

$\sqrt[3]{\frac{{(3 a)}^{3} a}{{(2 b)}^{3} \cdot 1}}$

Rearrange the fraction $\frac{{(3 a)}^{3} a}{{(2 b)}^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{3 a}{2 b})}^{3} a}$

Step 2

Pull terms out from under the radical.

$\frac{3 a}{2 b} \sqrt[3]{a}$

Step 3

Combine $\frac{3 a}{2 b}$ and $\sqrt[3]{a}$ .

$\frac{3 a \sqrt[3]{a}}{2 b}$