Solve n^7*n^3/n^6

$$\frac { n ^ { 7 } \times n ^ { 3 } } { n ^ { 6 } }$$

Evaluate

$$n^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{n^{10}}{n^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 10 to get 4.

$$n^{4}$$

Differentiate w.r.t. n

$$4n^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{10}}{n^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 10 to get 4.

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

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

$$4n^{4-1}$$

Subtract 1 from 4.

$$4n^{3}$$