Solve 32a^3b^2/8a^5b

$$\frac { 32 a ^ { 3 } b ^ { 2 } } { 8 a ^ { 5 } b }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{32^{1}a^{3}b^{2}}{8^{1}a^{5}b^{1}}$$

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

$$\frac{32^{1}}{8^{1}}a^{3-5}b^{2-1}$$

Subtract 5 from 3.

$$\frac{32^{1}}{8^{1}}a^{-2}b^{2-1}$$

Subtract 1 from 2.

$$\frac{32^{1}}{8^{1}}\times \frac{1}{a^{2}}b^{1}$$

Divide 32 by 8.

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

Differentiate w.r.t. b

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