Solve 12ab^2/15a^2b

$$\frac { 12 a b ^ { 2 } } { 15 a ^ { 2 } b }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}a^{1}b^{2}}{15^{1}a^{2}b^{1}}$$

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

$$\frac{12^{1}}{15^{1}}a^{1-2}b^{2-1}$$

Subtract 2 from 1.

$$\frac{12^{1}}{15^{1}}\times \frac{1}{a}b^{2-1}$$

Subtract 1 from 2.

$$\frac{12^{1}}{15^{1}}\times \frac{1}{a}b^{1}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

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

Differentiate w.r.t. a

$$-\frac{4b}{5a^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12b^{2}}{15b}a^{1-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-\frac{4b}{5}\right)a^{-2}$$