Solve b^5*(b^3)^3

$$b ^ { 5 } \times ( b ^ { 3 } ) ^ { 3 }$$

Evaluate

$$b^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$b^{5}b^{9}$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$b^{14}$$

Differentiate w.r.t. b

$$14b^{13}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{5}b^{9})$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{14})$$

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

$$14b^{14-1}$$

Subtract 1 from 14.

$$14b^{13}$$