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

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

Evaluate

$$\frac{1}{a^{7}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{-4}a^{2}a^{-5}$$

Use the Multiplication Rule for Exponents.

$$a^{-4+2-5}$$

Add the exponents -4 and 2.

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

Add the exponents -2 and -5.

$$a^{-7}$$

Differentiate w.r.t. a

$$-\frac{7}{a^{8}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{-2}a^{-5})$$

To multiply powers of the same base, add their exponents. Add -2 and -5 to get -7.

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

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

$$-7a^{-7-1}$$

Subtract 1 from -7.

$$-7a^{-8}$$