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

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

Evaluate

$$\frac{4\left(ab\right)^{2}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 4.

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

Subtract 2 from 4.

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

Divide 4 by 3.

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

Differentiate w.r.t. a

$$\frac{8ab^{2}}{3}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{8b^{2}}{3}a^{1}$$

For any term t, t^{1}=t.

$$\frac{8b^{2}}{3}a$$