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

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

Evaluate

$$\frac{1}{a^{6}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{-5}a^{2}a^{-3}$$

Use the Multiplication Rule for Exponents.

$$a^{-5+2-3}$$

Add the exponents -5 and 2.

$$a^{-3-3}$$

Add the exponents -3 and -3.

$$a^{-6}$$

Differentiate w.r.t. a

$$-\frac{6}{a^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and 2 to get -3.

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

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

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

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

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

Subtract 1 from -6.

$$-6a^{-7}$$