Solve (a^3)^2(a^1)^-1

$$( a ^ { 3 } ) ^ { 2 } ( a ^ { 1 } ) ^ { - 1 }$$

Evaluate

$$a^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}\left(a^{1}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 1 and -1 to get -1.

$$a^{6}a^{-1}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$a^{5}$$

Differentiate w.r.t. a

$$5a^{4}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}\left(a^{1}\right)^{-1})$$

To raise a power to another power, multiply the exponents. Multiply 1 and -1 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}a^{-1})$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{5})$$

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

$$5a^{5-1}$$

Subtract 1 from 5.

$$5a^{4}$$