Solve x^3*x^6*x^7=

$$x ^ { 3 } \cdot x ^ { 6 } \cdot x ^ { 7 } =$$

Evaluate

$$x^{16}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{6}x^{7}$$

Use the Multiplication Rule for Exponents.

$$x^{3+6+7}$$

Add the exponents 3 and 6.

$$x^{9+7}$$

Add the exponents 9 and 7.

$$x^{16}$$

Differentiate w.r.t. x

$$16x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{9}x^{7})$$

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{16})$$

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

$$16x^{16-1}$$

Subtract 1 from 16.

$$16x^{15}$$