Solve 20a^2b/25ab

$$\frac { 20 a ^ { 2 } b } { 25 a b }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{20^{1}a^{2}b^{1}}{25^{1}a^{1}b^{1}}$$

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

$$\frac{20^{1}}{25^{1}}a^{2-1}b^{1-1}$$

Subtract 1 from 2.

$$\frac{20^{1}}{25^{1}}a^{1}b^{1-1}$$

Subtract 1 from 1.

$$\frac{20^{1}}{25^{1}}ab^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{20^{1}}{25^{1}}a$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

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

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{20b}{25b}a^{2-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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.

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