Solve n^6/n^2*n^-9

$$\frac { n ^ { 6 } } { n ^ { 2 } \cdot n ^ { - 9 } }$$

Evaluate

$$n^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -9 to get -7.

$$\frac{n^{6}}{n^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -7 from 6 to get 13.

$$n^{13}$$

Differentiate w.r.t. n

$$13n^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and -9 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{6}}{n^{-7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -7 from 6 to get 13.

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

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

$$13n^{13-1}$$

Subtract 1 from 13.

$$13n^{12}$$