Solve t^-7*t^4*t^-6

$$t ^ { - 7 } \cdot t ^ { 4 } \cdot t ^ { - 6 }$$

Evaluate

$$\frac{1}{t^{9}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$t^{-7}t^{4}t^{-6}$$

Use the Multiplication Rule for Exponents.

$$t^{-7+4-6}$$

Add the exponents -7 and 4.

$$t^{-3-6}$$

Add the exponents -3 and -6.

$$t^{-9}$$

Differentiate w.r.t. t

$$-\frac{9}{t^{10}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{-3}t^{-6})$$

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

$$-9t^{-10}$$