Simplify (y*y^(1/3))^(3/2)

${(y \cdot y^{\frac{1}{3}})}^{\frac{3}{2}}$

Step 1

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

Multiply $y$ by $y^{\frac{1}{3}}$ .

Raise $y$ to the power of $1$ .

${(y^{1} \cdot y^{\frac{1}{3}})}^{\frac{3}{2}}$

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

${(y^{1 + \frac{1}{3}})}^{\frac{3}{2}}$

Write $1$ as a fraction with a common denominator.

${(y^{\frac{3}{3} + \frac{1}{3}})}^{\frac{3}{2}}$

Combine the numerators over the common denominator.

${(y^{\frac{3 + 1}{3}})}^{\frac{3}{2}}$

Add $3$ and $1$ .

${(y^{\frac{4}{3}})}^{\frac{3}{2}}$

Step 2

Multiply the exponents in ${(y^{\frac{4}{3}})}^{\frac{3}{2}}$ .

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

$y^{\frac{4}{3} \cdot \frac{3}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y^{\frac{2 (2)}{3} \cdot \frac{3}{2}}$

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$y^{2}$