Solve n^2/{n^frac{11{12}}}

$$\frac{ { n }^{ 2 } }{ { n }^{ \frac{ 11 }{ 12 } } }$$

Evaluate

$$n^{\frac{13}{12}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{n^{2}}{n^{\frac{11}{12}}}$$

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

$$n^{2-\frac{11}{12}}$$

Subtract \frac{11}{12} from 2.

$$n^{\frac{13}{12}}$$

Differentiate w.r.t. n

$$\frac{13\sqrt[12]{n}}{12}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{1}n^{2-\frac{11}{12}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{\frac{13}{12}})$$

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}.

$$\frac{13}{12}n^{\frac{13}{12}-1}$$

Do the arithmetic.

$$\frac{13}{12}\sqrt[12]{n}$$