Solve (a/b^-2)(b/a)

$$( \frac { a } { b ^ { - 2 } } ) ( \frac { b } { a } )$$

Evaluate

$$b^{3}$$

Solution Steps

Multiply \frac{a}{b^{-2}} times \frac{b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ab}{b^{-2}a}$$

Cancel out a in both numerator and denominator.

$$\frac{b}{b^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$b^{3}$$

Differentiate w.r.t. b

$$3b^{2}$$

Steps Using Definition of a Derivative

Multiply \frac{a}{b^{-2}} times \frac{b}{a} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{3})$$

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

$$3b^{3-1}$$

Subtract 1 from 3.

$$3b^{2}$$