Solve (b^4)^2b^2

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

Evaluate

$$b^{10}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$b^{10}$$

Differentiate w.r.t. b

$$10b^{9}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{10})$$

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

$$10b^{10-1}$$

Subtract 1 from 10.

$$10b^{9}$$