Solve q^-4*q^6*q^-3

$$q ^ { - 4 } \times q ^ { 6 } \times q ^ { - 3 }$$

Evaluate

$$\frac{1}{q}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$q^{-4}q^{6}q^{-3}$$

Use the Multiplication Rule for Exponents.

$$q^{-4+6-3}$$

Add the exponents -4 and 6.

$$q^{2-3}$$

Add the exponents 2 and -3.

$$\frac{1}{q}$$

Differentiate w.r.t. q

$$-\frac{1}{q^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{2}q^{-3})$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{-1})$$

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

$$-q^{-1-1}$$

Subtract 1 from -1.

$$-q^{-2}$$