Solve n^9/n^5

$$\frac { n ^ { 9 } } { n ^ { 5 } }$$

Evaluate

$$n^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{n^{9}}{n^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$n^{9-5}$$

Subtract 5 from 9.

$$n^{4}$$

Differentiate w.r.t. n

$$4n^{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{1}n^{9-5})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

$$4n^{3}$$