Solve 4ab^3/2a^2b^2=

$$\frac { 4 a b ^ { 3 } } { 2 a ^ { 2 } b ^ { 2 } } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}a^{1}b^{3}}{2^{1}a^{2}b^{2}}$$

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

$$\frac{4^{1}}{2^{1}}a^{1-2}b^{3-2}$$

Subtract 2 from 1.

$$\frac{4^{1}}{2^{1}}\times \frac{1}{a}b^{3-2}$$

Subtract 2 from 3.

$$\frac{4^{1}}{2^{1}}\times \frac{1}{a}b^{1}$$

Divide 4 by 2.

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

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.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4b^{3}}{2b^{2}}a^{1-2})$$

Do the arithmetic.

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

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}.

$$-2ba^{-1-1}$$

Do the arithmetic.

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