Solve w^2*w^-3/w^-4

$$\frac { w ^ { 2 } \times w ^ { - 3 } } { w ^ { - 4 } }$$

Evaluate

$$w^{3}$$

Solution Steps

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

$$\frac{w^{-1}}{w^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from -1 to get 3.

$$w^{3}$$

Differentiate w.r.t. w

$$3w^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{-1}}{w^{-4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from -1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{3})$$

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

$$3w^{3-1}$$

Subtract 1 from 3.

$$3w^{2}$$