Solve b^-4b^6b^7

$$b ^ { - 4 } b ^ { 6 } b ^ { 7 }$$

Evaluate

$$b^{9}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{-4}b^{6}b^{7}$$

Use the Multiplication Rule for Exponents.

$$b^{-4+6+7}$$

Add the exponents -4 and 6.

$$b^{2+7}$$

Add the exponents 2 and 7.

$$b^{9}$$

Differentiate w.r.t. b

$$9b^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{2}b^{7})$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

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

The derivative of ax^{n} is nax^{n-1}.

$$9b^{9-1}$$

Subtract 1 from 9.

$$9b^{8}$$