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

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

Evaluate

$$\frac{1}{a}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

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

Rewrite a^{-2} as a^{-3}a. Cancel out a^{-3} in both numerator and denominator.

$$\frac{1}{a}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-3}}{a^{-2}})$$

Rewrite a^{-2} as a^{-3}a. Cancel out a^{-3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a})$$

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

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

Subtract 1 from -1.

$$-a^{-2}$$