Solve a*b^5/a*b^2

$$\frac { a \times b ^ { 5 } } { a \times b ^ { 2 } }$$

Evaluate

$$b^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{1}b^{5}}{a^{1}b^{2}}$$

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

$$a^{1-1}b^{5-2}$$

Subtract 1 from 1.

$$a^{0}b^{5-2}$$

Subtract 2 from 5.

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

For any number a except 0, a^{0}=1.

$$b^{3}$$

Differentiate w.r.t. b

$$3b^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{a}{a}b^{5-2})$$

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.

$$3b^{2}$$