Solve x^7/3(x^5/3+x^-1/3)

$$x ^ { 7 / 3 } ( x ^ { 5 / 3 } + x ^ { - 1 / 3 } )$$

Evaluate

$$x^{4}+x^{2}$$

Solution Steps

Use the distributive property to multiply x^{\frac{7}{3}} by x^{\frac{5}{3}}+x^{-\frac{1}{3}}.

$$x^{\frac{7}{3}}x^{\frac{5}{3}}+x^{\frac{7}{3}}x^{-\frac{1}{3}}$$

To multiply powers of the same base, add their exponents. Add \frac{7}{3} and \frac{5}{3} to get 4.

$$x^{4}+x^{\frac{7}{3}}x^{-\frac{1}{3}}$$

To multiply powers of the same base, add their exponents. Add \frac{7}{3} and -\frac{1}{3} to get 2.

$$x^{4}+x^{2}$$

Factor

$$x^{2}\left(x^{2}+1\right)$$