Solve b^5:b^3=

$$b ^ { 5 } : b ^ { 3 } =$$

Evaluate

$$b^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$b^{5-3}$$

Subtract 3 from 5.

$$b^{2}$$

Differentiate w.r.t. b

$$2b$$

Solution Steps

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

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

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.

$$2b^{1}$$

For any term t, t^{1}=t.

$$2b$$