Solve n^6*n^2*n^3

$$n ^ { 6 } \cdot n ^ { 2 } \cdot n ^ { 3 }$$

Evaluate

$$n^{11}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$n^{6}n^{2}n^{3}$$

Use the Multiplication Rule for Exponents.

$$n^{6+2+3}$$

Add the exponents 6 and 2.

$$n^{8+3}$$

Add the exponents 8 and 3.

$$n^{11}$$

Differentiate w.r.t. n

$$11n^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

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

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

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

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

$$11n^{11-1}$$

Subtract 1 from 11.

$$11n^{10}$$