Solve 8u^2/10u

$$\frac { 8 u ^ { 2 } } { 10 u }$$

Evaluate

$$\frac{4u}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}u^{2}}{10^{1}u^{1}}$$

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

$$\frac{8^{1}u^{2-1}}{10^{1}}$$

Subtract 1 from 2.

$$\frac{8^{1}u^{1}}{10^{1}}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}u^{1}$$

For any term t, t^{1}=t.

$$\frac{4}{5}u$$

Differentiate w.r.t. u

$$\frac{4}{5} = 0.8$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{8}{10}u^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{4}{5}u^{1})$$

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}.

$$\frac{4}{5}u^{1-1}$$

Do the arithmetic.

$$\frac{4}{5}u^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{4}{5}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{4}{5}$$