Solve b/b^4

$$\frac { b } { b ^ { 4 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{1}}{b^{4}}$$

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

$$b^{1-4}$$

Subtract 4 from 1.

$$b^{-3}$$

Differentiate w.r.t. b

$$-\frac{3}{b^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{1-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-3b^{-4}$$