Solve b^7*b^0*b^4

$$b ^ { 7 } \times b ^ { 0 } \times b ^ { 4 }$$

Evaluate

$$b^{11}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{7}b^{0}b^{4}$$

Use the Multiplication Rule for Exponents.

$$b^{7+4}$$

Add the exponents 7 and 4.

$$b^{11}$$

Differentiate w.r.t. b

$$11b^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{7}b^{4})$$

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

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

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

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

Subtract 1 from 11.

$$11b^{10}$$