Solve b^-0/b^7

$$\frac { b ^ { - 0 } } { b ^ { 7 } }$$

Evaluate

$$\frac{1}{b^{7}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{0}}{b^{7}}$$

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

$$b^{-7}$$

Differentiate w.r.t. b

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

Steps Using Chain Rule

Rewrite b^{7} as b^{0}b^{7}. Cancel out b^{0} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{b^{7}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

$$-\left(b^{7}\right)^{-2}\times 7b^{7-1}$$

Simplify.

$$-7b^{6}\left(b^{7}\right)^{-2}$$