Solve {a}^frac{1{3}}{a}^-frac{3{3}}a^2a^0

$${ a }^{ \frac{ 1 }{ 3 } } { a }^{ - \frac{ 3 }{ 3 } } { a }^{ 2 } { a }^{ 0 }$$

Differentiate w.r.t. a

$$\frac{4\sqrt[3]{a}}{3}$$

Steps Using Definition of a Derivative

Divide 3 by 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{1}{3}}a^{-1}a^{2}a^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{7}{3}}a^{-1}a^{0})$$

To multiply powers of the same base, add their exponents. Add \frac{7}{3} and 0 to get \frac{7}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{7}{3}}a^{-1})$$

To multiply powers of the same base, add their exponents. Add \frac{7}{3} and -1 to get \frac{4}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{4}{3}})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{4}{3}a^{\frac{4}{3}-1}$$

Subtract 1 from \frac{4}{3}.

$$\frac{4}{3}\sqrt[3]{a}$$

Evaluate

$$a^{\frac{4}{3}}$$