Solve 24ab^2/36a^2b

$$\frac { 24 a b ^ { 2 } } { 36 a ^ { 2 } b }$$

Evaluate

$$\frac{2b}{3a}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{24^{1}a^{1}b^{2}}{36^{1}a^{2}b^{1}}$$

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

$$\frac{24^{1}}{36^{1}}a^{1-2}b^{2-1}$$

Subtract 2 from 1.

$$\frac{24^{1}}{36^{1}}\times \frac{1}{a}b^{2-1}$$

Subtract 1 from 2.

$$\frac{24^{1}}{36^{1}}\times \frac{1}{a}b^{1}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{2}{3}\times \frac{1}{a}b$$

Differentiate w.r.t. a

$$-\frac{2b}{3a^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{24b^{2}}{36b}a^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2b}{3}\times \frac{1}{a})$$

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}.

$$-\frac{2b}{3}a^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{2b}{3}\right)a^{-2}$$