Solve n^7/n^-4*n^8

$$\frac { n ^ { 7 } } { n ^ { - 4 } \cdot n ^ { 8 } }$$

Evaluate

$$n^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and 8 to get 4.

$$\frac{n^{7}}{n^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$n^{3}$$

Differentiate w.r.t. n

$$3n^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -4 and 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{7}}{n^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

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

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

$$3n^{3-1}$$

Subtract 1 from 3.

$$3n^{2}$$