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

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

Evaluate

$$b^{3}$$

Solution Steps

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

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

Calculate a to the power of 0 and get 1.

$$1b^{3}$$

For any term t, t\times 1=t and 1t=t.

$$b^{3}$$

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.

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

Calculate a to the power of 0 and get 1.

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

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

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

Subtract 1 from 3.

$$3b^{2}$$