Solve b^9divb^2

$$b ^ { 9 } \div b ^ { 2 }$$

Evaluate

$$b^{7}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{9}}{b^{2}}$$

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

$$b^{9-2}$$

Subtract 2 from 9.

$$b^{7}$$

Differentiate w.r.t. b

$$7b^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{9-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{7})$$

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}.

$$7b^{7-1}$$

Do the arithmetic.

$$7b^{6}$$