Convert to Radical Form y^(1/3)*y^(2/5)

$y^{\frac{1}{3}} \cdot y^{\frac{2}{5}}$

Multiply $y^{\frac{1}{3}}$ by $y^{\frac{2}{5}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y^{\frac{1}{3} + \frac{2}{5}}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y^{\frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5}}$

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y^{\frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{3}{3}}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$y^{\frac{5}{3 \cdot 5} + \frac{2}{5} \cdot \frac{3}{3}}$

Multiply $3$ by $5$ .

$y^{\frac{5}{15} + \frac{2}{5} \cdot \frac{3}{3}}$

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$y^{\frac{5}{15} + \frac{2 \cdot 3}{5 \cdot 3}}$

Multiply $5$ by $3$ .

$y^{\frac{5}{15} + \frac{2 \cdot 3}{15}}$

Combine the numerators over the common denominator.

$y^{\frac{5 + 2 \cdot 3}{15}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$y^{\frac{5 + 6}{15}}$

Add $5$ and $6$ .

$y^{\frac{11}{15}}$

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[15]{y^{11}}$