Solve a^-2/3(a^5/4-a^3)

$$a ^ { - 2 / 3 } ( a ^ { 5 / 4 } - a ^ { 3 } )$$

Evaluate

$$a^{\frac{7}{12}}-a^{\frac{7}{3}}$$

Solution Steps

Use the distributive property to multiply a^{-\frac{2}{3}} by a^{\frac{5}{4}}-a^{3}.

$$a^{-\frac{2}{3}}a^{\frac{5}{4}}-a^{-\frac{2}{3}}a^{3}$$

To multiply powers of the same base, add their exponents. Add -\frac{2}{3} and \frac{5}{4} to get \frac{7}{12}.

$$a^{\frac{7}{12}}-a^{-\frac{2}{3}}a^{3}$$

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

$$a^{\frac{7}{12}}-a^{\frac{7}{3}}$$

Factor

$$a^{\frac{7}{12}}\left(1-a^{\frac{7}{4}}\right)$$