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

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

Apply basic rules of exponents.

Apply the product rule to $\frac{a^{\frac{2}{5}}}{b^{\frac{1}{5}}}$ .

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

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

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

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

$\frac{a^{2}}{b^{\frac{1}{5} \cdot 5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{a^{2}}{b^{\frac{1}{5} \cdot 5}}$

Rewrite the expression.

$\frac{a^{2}}{b^{1}}$

Simplify.

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