Solve y^9*y^8/y^4

$$\frac { y ^ { 9 } \cdot y ^ { 8 } } { y ^ { 4 } }$$

Evaluate

$$y^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$\frac{y^{17}}{y^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 17 to get 13.

$$y^{13}$$

Differentiate w.r.t. y

$$13y^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{17}}{y^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 17 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{13})$$

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

$$13y^{13-1}$$

Subtract 1 from 13.

$$13y^{12}$$