Solve a^9*a^4*a^-15

$$a ^ { 9 } \cdot a ^ { 4 } \cdot a ^ { - 15 }$$

Evaluate

$$\frac{1}{a^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{9}a^{4}a^{-15}$$

Use the Multiplication Rule for Exponents.

$$a^{9+4-15}$$

Add the exponents 9 and 4.

$$a^{13-15}$$

Add the exponents 13 and -15.

$$a^{-2}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{13}a^{-15})$$

To multiply powers of the same base, add their exponents. Add 13 and -15 to get -2.

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

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

$$-2a^{-2-1}$$

Subtract 1 from -2.

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