Simplify the Radical Expression (5a^3b^2)^(2/3)

${(5 a^{3} b^{2})}^{\frac{2}{3}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $5 a^{3} b^{2}$ .

${(5 a^{3})}^{\frac{2}{3}} {(b^{2})}^{\frac{2}{3}}$

Apply the product rule to $5 a^{3}$ .

$5^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}} {(b^{2})}^{\frac{2}{3}}$

Multiply the exponents in ${(a^{3})}^{\frac{2}{3}}$ .

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

$5^{\frac{2}{3}} a^{3 (\frac{2}{3})} {(b^{2})}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{\frac{2}{3}} a^{3 (\frac{2}{3})} {(b^{2})}^{\frac{2}{3}}$

Rewrite the expression.

$5^{\frac{2}{3}} a^{2} {(b^{2})}^{\frac{2}{3}}$

Multiply the exponents in ${(b^{2})}^{\frac{2}{3}}$ .

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

$5^{\frac{2}{3}} a^{2} b^{2 (\frac{2}{3})}$

Multiply $2 (\frac{2}{3})$ .

Combine $2$ and $\frac{2}{3}$ .

$5^{\frac{2}{3}} a^{2} b^{\frac{2 \cdot 2}{3}}$

Multiply $2$ by $2$ .

$5^{\frac{2}{3}} a^{2} b^{\frac{4}{3}}$

Reorder factors in $5^{\frac{2}{3}} a^{2} b^{\frac{4}{3}}$ .

$a^{2} \cdot 5^{\frac{2}{3}} b^{\frac{4}{3}}$