Solve n^5*n^2*n^4

$$n ^ { 5 } \cdot n ^ { 2 } \cdot n ^ { 4 }$$

Evaluate

$$n^{11}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$n^{5}n^{2}n^{4}$$

Use the Multiplication Rule for Exponents.

$$n^{5+2+4}$$

Add the exponents 5 and 2.

$$n^{7+4}$$

Add the exponents 7 and 4.

$$n^{11}$$

Differentiate w.r.t. n

$$11n^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

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

$$11n^{10}$$