Solve 6ab^5/9a^3b^2=

$$\frac { 6 a b ^ { 5 } } { 9 a ^ { 3 } b ^ { 2 } } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}a^{1}b^{5}}{9^{1}a^{3}b^{2}}$$

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

$$\frac{6^{1}}{9^{1}}a^{1-3}b^{5-2}$$

Subtract 3 from 1.

$$\frac{6^{1}}{9^{1}}a^{-2}b^{5-2}$$

Subtract 2 from 5.

$$\frac{6^{1}}{9^{1}}\times \frac{1}{a^{2}}b^{3}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

Differentiate w.r.t. b

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