Solve (b^4)(b^2)(b^6)=

$$( b ^ { 4 } ) ( b ^ { 2 } ) ( b ^ { 6 } ) =$$

Evaluate

$$b^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{4}b^{2}b^{6}$$

Use the Multiplication Rule for Exponents.

$$b^{4+2+6}$$

Add the exponents 4 and 2.

$$b^{6+6}$$

Add the exponents 6 and 6.

$$b^{12}$$

Differentiate w.r.t. b

$$12b^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{6}b^{6})$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{12})$$

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

$$12b^{12-1}$$

Subtract 1 from 12.

$$12b^{11}$$