Solve w^5*w^8/w^4

$$\frac { w ^ { 5 } \times w ^ { 8 } } { w ^ { 4 } }$$

Evaluate

$$w^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$\frac{w^{13}}{w^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 13 to get 9.

$$w^{9}$$

Differentiate w.r.t. w

$$9w^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{13}}{w^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 13 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{9})$$

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

$$9w^{9-1}$$

Subtract 1 from 9.

$$9w^{8}$$