Solve g^2*g^-6*g

$$g ^ { 2 } \cdot g ^ { - 6 } \cdot g$$

Evaluate

$$\frac{1}{g^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$g^{2}g^{-6}g^{1}$$

Use the Multiplication Rule for Exponents.

$$g^{2-6+1}$$

Add the exponents 2 and -6.

$$g^{-4+1}$$

Add the exponents -4 and 1.

$$g^{-3}$$

Differentiate w.r.t. g

$$-\frac{3}{g^{4}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(g^{-4}g)$$

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

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

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

$$-3g^{-3-1}$$

Subtract 1 from -3.

$$-3g^{-4}$$