Solve 32k^2/80k

$$\frac { 32 k ^ { 2 } } { 80 k }$$

Evaluate

$$\frac{2k}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{32^{1}k^{2}}{80^{1}k^{1}}$$

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

$$\frac{32^{1}k^{2-1}}{80^{1}}$$

Subtract 1 from 2.

$$\frac{32^{1}k^{1}}{80^{1}}$$

Reduce the fraction \frac{32}{80} to lowest terms by extracting and canceling out 16.

$$\frac{2}{5}k^{1}$$

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

$$\frac{2}{5}k$$

Differentiate w.r.t. k

$$\frac{2}{5} = 0.4$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{32}{80}k^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{2}{5}k^{1})$$

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}.

$$\frac{2}{5}k^{1-1}$$

Do the arithmetic.

$$\frac{2}{5}k^{0}$$

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

$$\frac{2}{5}\times 1$$

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

$$\frac{2}{5}$$