Solve a^-5*a^9*a^-8

$$a ^ { - 5 } \cdot a ^ { 9 } \cdot a ^ { - 8 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{-5}a^{9}a^{-8}$$

Use the Multiplication Rule for Exponents.

$$a^{-5+9-8}$$

Add the exponents -5 and 9.

$$a^{4-8}$$

Add the exponents 4 and -8.

$$a^{-4}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and 9 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{-8})$$

To multiply powers of the same base, add their exponents. Add 4 and -8 to get -4.

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

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

$$-4a^{-4-1}$$

Subtract 1 from -4.

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