Solve 4p^2q/8pq^2

$$\frac { 4 p ^ { 2 } q } { 8 p q ^ { 2 } }$$

Evaluate

$$\frac{p}{2q}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}p^{2}q^{1}}{8^{1}p^{1}q^{2}}$$

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

$$\frac{4^{1}}{8^{1}}p^{2-1}q^{1-2}$$

Subtract 1 from 2.

$$\frac{4^{1}}{8^{1}}p^{1}q^{1-2}$$

Subtract 2 from 1.

$$\frac{4^{1}}{8^{1}}p\times \frac{1}{q}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}p\times \frac{1}{q}$$

Differentiate w.r.t. q

$$-\frac{p}{2q^{2}}$$