Solve t^3(t)(t^3)=

$$t ^ { 3 } ( t ) ( t ^ { 3 } ) =$$

Evaluate

$$t^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$t^{3}t^{1}t^{3}$$

Use the Multiplication Rule for Exponents.

$$t^{3+1+3}$$

Add the exponents 3 and 1.

$$t^{4+3}$$

Add the exponents 4 and 3.

$$t^{7}$$

Differentiate w.r.t. t

$$7t^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{4}t^{3})$$

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

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

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

$$7t^{7-1}$$

Subtract 1 from 7.

$$7t^{6}$$