Solve w^5*w^-7*w

$$w ^ { 5 } \cdot w ^ { - 7 } \cdot w$$

Evaluate

$$\frac{1}{w}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$w^{5}w^{-7}w^{1}$$

Use the Multiplication Rule for Exponents.

$$w^{5-7+1}$$

Add the exponents 5 and -7.

$$w^{-2+1}$$

Add the exponents -2 and 1.

$$\frac{1}{w}$$

Differentiate w.r.t. w

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -7 to get -2.

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

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

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

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

$$-w^{-1-1}$$

Subtract 1 from -1.

$$-w^{-2}$$