Solve b^-5/a^0b^-8

$$\frac { b ^ { - 5 } } { a ^ { 0 } b ^ { - 8 } }$$

Evaluate

$$b^{3}$$

Solution Steps

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

$$\frac{b^{3}}{a^{0}}$$

Calculate a to the power of 0 and get 1.

$$\frac{b^{3}}{1}$$

Anything divided by one gives itself.

$$b^{3}$$

Differentiate w.r.t. b

$$3b^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{3}}{a^{0}})$$

Calculate a to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{3}}{1})$$

Anything divided by one gives itself.

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

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

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

Subtract 1 from 3.

$$3b^{2}$$