Solve (2)-3a/b*frac{ab^{2}}{-a^3b^2}div(-3b/a^2)^2

$$( 2 ) \frac { - 3 a } { b } \cdot \frac { a b ^ { 2 } } { - a ^ { 3 } b ^ { 2 } } \div ( - \frac { 3 b } { a ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{2\times \left(\frac{a}{b}\right)^{3}}{3}$$

Short Solution Steps

Cancel out b^{2} in both numerator and denominator.

$$\frac{2\times \frac{-3a}{b}\times \frac{a}{-a^{3}}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Express 2\times \frac{-3a}{b} as a single fraction.

$$\frac{\frac{2\left(-3\right)a}{b}\times \frac{a}{-a^{3}}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Multiply \frac{2\left(-3\right)a}{b} times \frac{a}{-a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\left(-3\right)aa}{b\left(-a^{3}\right)}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Calculate -\frac{3b}{a^{2}} to the power of 2 and get \left(\frac{3b}{a^{2}}\right)^{2}.

$$\frac{\frac{2\left(-3\right)aa}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Multiply a and a to get a^{2}.

$$\frac{\frac{2\left(-3\right)a^{2}}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Multiply 2 and -3 to get -6.

$$\frac{\frac{-6a^{2}}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Factor the expressions that are not already factored in \frac{-6a^{2}}{b\left(-a^{3}\right)}.

$$\frac{\frac{-6a^{2}}{-ba^{3}}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{\frac{-6}{-ab}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

To raise \frac{3b}{a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{-6}{-ab}}{\frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}}}$$

Divide \frac{-6}{-ab} by \frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}} by multiplying \frac{-6}{-ab} by the reciprocal of \frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}}.

$$\frac{-6\left(a^{2}\right)^{2}}{-ab\times \left(3b\right)^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{6\left(a^{2}\right)^{2}}{ab\times \left(3b\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{6a^{4}}{ab\times \left(3b\right)^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{6a^{3}}{b\times \left(3b\right)^{2}}$$

Expand \left(3b\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Cancel out 3 in both numerator and denominator.

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

Expand

$$\frac{2\times \left(\frac{a}{b}\right)^{3}}{3}$$

Short Solution Steps

Cancel out b^{2} in both numerator and denominator.

$$\frac{2\times \frac{-3a}{b}\times \frac{a}{-a^{3}}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Express 2\times \frac{-3a}{b} as a single fraction.

$$\frac{\frac{2\left(-3\right)a}{b}\times \frac{a}{-a^{3}}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Multiply \frac{2\left(-3\right)a}{b} times \frac{a}{-a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\left(-3\right)aa}{b\left(-a^{3}\right)}}{\left(-\frac{3b}{a^{2}}\right)^{2}}$$

Calculate -\frac{3b}{a^{2}} to the power of 2 and get \left(\frac{3b}{a^{2}}\right)^{2}.

$$\frac{\frac{2\left(-3\right)aa}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Multiply a and a to get a^{2}.

$$\frac{\frac{2\left(-3\right)a^{2}}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Multiply 2 and -3 to get -6.

$$\frac{\frac{-6a^{2}}{b\left(-a^{3}\right)}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Factor the expressions that are not already factored in \frac{-6a^{2}}{b\left(-a^{3}\right)}.

$$\frac{\frac{-6a^{2}}{-ba^{3}}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{\frac{-6}{-ab}}{\left(\frac{3b}{a^{2}}\right)^{2}}$$

To raise \frac{3b}{a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{-6}{-ab}}{\frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}}}$$

Divide \frac{-6}{-ab} by \frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}} by multiplying \frac{-6}{-ab} by the reciprocal of \frac{\left(3b\right)^{2}}{\left(a^{2}\right)^{2}}.

$$\frac{-6\left(a^{2}\right)^{2}}{-ab\times \left(3b\right)^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{6\left(a^{2}\right)^{2}}{ab\times \left(3b\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{6a^{4}}{ab\times \left(3b\right)^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{6a^{3}}{b\times \left(3b\right)^{2}}$$

Expand \left(3b\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Cancel out 3 in both numerator and denominator.

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