Simplify cube root of (5a^2b)^6

$\sqrt[3]{{(5 a^{2} b)}^{6}}$

Step 1

Simplify the expression.

Apply the product rule to $5 a^{2} b$ .

$\sqrt[3]{{(5 a^{2})}^{6} b^{6}}$

Apply the product rule to $5 a^{2}$ .

$\sqrt[3]{5^{6} {(a^{2})}^{6} b^{6}}$

Raise $5$ to the power of $6$ .

$\sqrt[3]{15625 {(a^{2})}^{6} b^{6}}$

Multiply the exponents in ${(a^{2})}^{6}$ .

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

$\sqrt[3]{15625 a^{2 \cdot 6} b^{6}}$

Multiply $2$ by $6$ .

$\sqrt[3]{15625 a^{12} b^{6}}$

Step 2

Rewrite $15625 a^{12} b^{6}$ as ${(25 a^{4} b^{2})}^{3}$ .

$\sqrt[3]{{(25 a^{4} b^{2})}^{3}}$

Step 3

Pull terms out from under the radical, assuming real numbers.

$25 a^{4} b^{2}$