Solve b*b^2*b^3

$$b \cdot b ^ { 2 } \cdot b ^ { 3 }$$

Evaluate

$$b^{6}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{1}b^{2}b^{3}$$

Use the Multiplication Rule for Exponents.

$$b^{1+2+3}$$

Add the exponents 1 and 2.

$$b^{3+3}$$

Add the exponents 3 and 3.

$$b^{6}$$

Differentiate w.r.t. b

$$6b^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

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

$$6b^{6-1}$$

Subtract 1 from 6.

$$6b^{5}$$