Solve (1)10a^3b/4ab^2

$$( 1 ) \frac { 10 a ^ { 3 } b } { 4 a b ^ { 2 } }$$

Evaluate

$$\frac{5a^{2}}{2b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}a^{3}b^{1}}{4^{1}a^{1}b^{2}}$$

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

$$\frac{10^{1}}{4^{1}}a^{3-1}b^{1-2}$$

Subtract 1 from 3.

$$\frac{10^{1}}{4^{1}}a^{2}b^{1-2}$$

Subtract 2 from 1.

$$\frac{10^{1}}{4^{1}}a^{2}\times \frac{1}{b}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}a^{2}\times \frac{1}{b}$$

Differentiate w.r.t. b

$$-\frac{5\times \left(\frac{a}{b}\right)^{2}}{2}$$