Solve -8a^3b^5/4a^4b^4

$$\frac { - 8 a ^ { 3 } b ^ { 5 } } { 4 a ^ { 4 } b ^ { 4 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-8\right)^{1}a^{3}b^{5}}{4^{1}a^{4}b^{4}}$$

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

$$\frac{\left(-8\right)^{1}}{4^{1}}a^{3-4}b^{5-4}$$

Subtract 4 from 3.

$$\frac{\left(-8\right)^{1}}{4^{1}}\times \frac{1}{a}b^{5-4}$$

Subtract 4 from 5.

$$\frac{\left(-8\right)^{1}}{4^{1}}\times \frac{1}{a}b^{1}$$

Divide -8 by 4.

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

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{8b^{5}}{4b^{4}}\right)a^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-2b\right)\times \frac{1}{a})$$

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}.

$$-\left(-2b\right)a^{-1-1}$$

Do the arithmetic.

$$2ba^{-2}$$