Solve w^7/w^-6*w^-7

$$\frac { w ^ { 7 } } { w ^ { - 6 } \cdot w ^ { - 7 } }$$

Evaluate

$$w^{20}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -7 to get -13.

$$\frac{w^{7}}{w^{-13}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -13 from 7 to get 20.

$$w^{20}$$

Differentiate w.r.t. w

$$20w^{19}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and -7 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{7}}{w^{-13}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -13 from 7 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{20})$$

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

$$20w^{20-1}$$

Subtract 1 from 20.

$$20w^{19}$$