Solve 2b^3*(b^4)^2=

$$2 b ^ { 3 } \cdot ( b ^ { 4 } ) ^ { 2 } =$$

Evaluate

$$2b^{11}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2b^{3}b^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$2b^{11}$$

Differentiate w.r.t. b

$$22b^{10}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{3}b^{8})$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{11})$$

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

$$11\times 2b^{11-1}$$

Multiply 11 times 2.

$$22b^{11-1}$$

Subtract 1 from 11.

$$22b^{10}$$