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

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 3 from 2.

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

Subtract 3 from 4.

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

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.

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

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.

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