Solve b^3/b^5

$$\frac { b ^ { 3 } } { b ^ { 5 } }$$

Evaluate

$$\frac{1}{b^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{3}}{b^{5}}$$

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

$$b^{3-5}$$

Subtract 5 from 3.

$$b^{-2}$$

Differentiate w.r.t. b

$$-\frac{2}{b^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{3-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-2})$$

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}.

$$-2b^{-2-1}$$

Do the arithmetic.

$$-2b^{-3}$$