Solve y^2/3(y^1/3+y^-2/3)

$$y ^ { 2 / 3 } ( y ^ { 1 / 3 } + y ^ { - 2 / 3 } )$$

Evaluate

$$y+1$$

Solution Steps

Use the distributive property to multiply y^{\frac{2}{3}} by y^{\frac{1}{3}}+y^{-\frac{2}{3}}.

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

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and \frac{1}{3} to get 1.

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

Multiply y^{\frac{2}{3}} and y^{-\frac{2}{3}} to get 1.

$$y^{1}+1$$

Calculate y to the power of 1 and get y.

$$y+1$$

Factor

$$y+1$$