Simplify (y+y^2)/(y^(-2/3))

$\frac{y + y^{2}}{y^{- \frac{2}{3}}}$

Move $y^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Apply the distributive property.

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

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

Multiply $y$ by $y^{\frac{2}{3}}$ .

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

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

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

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

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

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

Combine $2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$y^{\frac{5}{3}} + y^{\frac{6 + 2}{3}}$

Add $6$ and $2$ .

$y^{\frac{5}{3}} + y^{\frac{8}{3}}$