Simplify (3x^0y^(1/5))^(5/3)

${(3 x^{0} y^{\frac{1}{5}})}^{\frac{5}{3}}$

Anything raised to $0$ is $1$ .

${(3 \cdot 1 y^{\frac{1}{5}})}^{\frac{5}{3}}$

Multiply $3$ by $1$ .

${(3 y^{\frac{1}{5}})}^{\frac{5}{3}}$

Apply the product rule to $3 y^{\frac{1}{5}}$ .

$3^{\frac{5}{3}} {(y^{\frac{1}{5}})}^{\frac{5}{3}}$

Multiply the exponents in ${(y^{\frac{1}{5}})}^{\frac{5}{3}}$ .

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

$3^{\frac{5}{3}} y^{\frac{1}{5} \cdot \frac{5}{3}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$3^{\frac{5}{3}} y^{\frac{1}{5} \cdot \frac{5}{3}}$

Rewrite the expression.

$3^{\frac{5}{3}} y^{\frac{1}{3}}$