Solve b^-7/b^-8

$$\frac { b ^ { - 7 } } { b ^ { - 8 } }$$

Evaluate

$$b$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -8 from -7 to get 1.

$$b^{1}$$

Calculate b to the power of 1 and get b.

$$b$$

Differentiate w.r.t. b

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{-7-\left(-8\right)})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$b^{1-1}$$

Do the arithmetic.

$$b^{0}$$

For any term t except 0, t^{0}=1.

$$1$$