Solve b^2/b^frac{1{2}}

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract \frac{1}{2} from 2.

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

Differentiate w.r.t. b

$$\frac{3\sqrt{b}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{2-\frac{1}{2}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{\frac{3}{2}})$$

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}.

$$\frac{3}{2}b^{\frac{3}{2}-1}$$

Do the arithmetic.

$$\frac{3}{2}\sqrt{b}$$