Solve u^14/u^frac{9{10}}

$$\frac { u ^ { 14 } } { u ^ { \frac { 9 } { 10 } } }$$

Evaluate

$$u^{\frac{131}{10}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{u^{14}}{u^{\frac{9}{10}}}$$

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

$$u^{14-\frac{9}{10}}$$

Subtract \frac{9}{10} from 14.

$$u^{\frac{131}{10}}$$

Differentiate w.r.t. u

$$\frac{131u^{\frac{121}{10}}}{10}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{14-\frac{9}{10}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{131}{10}})$$

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}.

$$\frac{131}{10}u^{\frac{131}{10}-1}$$

Do the arithmetic.

$$\frac{131}{10}u^{\frac{121}{10}}$$