Solve -9a^2b^4/15a^3b^3

$$\frac{ -9 { a }^{ 2 } { b }^{ 4 } }{ 15 { a }^{ 3 } { b }^{ 3 } }$$

Evaluate

$$-\frac{3b}{5a}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-9\right)^{1}a^{2}b^{4}}{15^{1}a^{3}b^{3}}$$

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

$$\frac{\left(-9\right)^{1}}{15^{1}}a^{2-3}b^{4-3}$$

Subtract 3 from 2.

$$\frac{\left(-9\right)^{1}}{15^{1}}\times \frac{1}{a}b^{4-3}$$

Subtract 3 from 4.

$$\frac{\left(-9\right)^{1}}{15^{1}}\times \frac{1}{a}b^{1}$$

Reduce the fraction \frac{-9}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{5}\times \frac{1}{a}b$$

Differentiate w.r.t. a

$$\frac{3b}{5a^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{9b^{4}}{15b^{3}}\right)a^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{3b}{5}\right)\times \frac{1}{a})$$

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}.

$$-\left(-\frac{3b}{5}\right)a^{-1-1}$$

Do the arithmetic.

$$\frac{3b}{5}a^{-2}$$