Simplify (a^2b^2)^(1/5)

${(a^{2} b^{2})}^{\frac{1}{5}}$

Step 1

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

${(a^{2})}^{\frac{1}{5}} {(b^{2})}^{\frac{1}{5}}$

Step 2

Multiply the exponents in ${(a^{2})}^{\frac{1}{5}}$ .

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

$a^{2 (\frac{1}{5})} {(b^{2})}^{\frac{1}{5}}$

Combine $2$ and $\frac{1}{5}$ .

$a^{\frac{2}{5}} {(b^{2})}^{\frac{1}{5}}$

Step 3

Multiply the exponents in ${(b^{2})}^{\frac{1}{5}}$ .

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

$a^{\frac{2}{5}} b^{2 (\frac{1}{5})}$

Combine $2$ and $\frac{1}{5}$ .

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