Solve t^3*t^4*t^2=

$$t ^ { 3 } \cdot t ^ { 4 } \cdot t ^ { 2 } =$$

Evaluate

$$t^{9}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$t^{3}t^{4}t^{2}$$

Use the Multiplication Rule for Exponents.

$$t^{3+4+2}$$

Add the exponents 3 and 4.

$$t^{7+2}$$

Add the exponents 7 and 2.

$$t^{9}$$

Differentiate w.r.t. t

$$9t^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{7}t^{2})$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{9})$$

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

$$9t^{9-1}$$

Subtract 1 from 9.

$$9t^{8}$$