Solve (1/3a^2b)^2*(-9ab)div(-1/2a^3b^2)

$$( \frac { 1 } { 3 } a ^ { 2 } b ) ^ { 2 } \cdot ( - 9 a b ) \div ( - \frac { 1 } { 2 } a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$2ba^{2}$$

Solution Steps

Cancel out ab in both numerator and denominator.

$$\frac{-9\times \left(\frac{1}{3}ba^{2}\right)^{2}}{-\frac{1}{2}ba^{2}}$$

Expand \left(\frac{1}{3}ba^{2}\right)^{2}.

$$\frac{-9\times \left(\frac{1}{3}\right)^{2}b^{2}\left(a^{2}\right)^{2}}{-\frac{1}{2}ba^{2}}$$

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

$$\frac{-9\times \left(\frac{1}{3}\right)^{2}b^{2}a^{4}}{-\frac{1}{2}ba^{2}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{-9\times \frac{1}{9}b^{2}a^{4}}{-\frac{1}{2}ba^{2}}$$

Multiply -9 and \frac{1}{9} to get -1.

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

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

$$\frac{-ba^{2}}{-\frac{1}{2}}$$

Divide -ba^{2} by -\frac{1}{2} by multiplying -ba^{2} by the reciprocal of -\frac{1}{2}.

$$\frac{-ba^{2}\times 2}{-1}$$

Cancel out -1 and -1.

$$ba^{2}\times 2$$

Expand

$$2ba^{2}$$

Solution Steps

Cancel out ab in both numerator and denominator.

$$\frac{-9\times \left(\frac{1}{3}ba^{2}\right)^{2}}{-\frac{1}{2}ba^{2}}$$

Expand \left(\frac{1}{3}ba^{2}\right)^{2}.

$$\frac{-9\times \left(\frac{1}{3}\right)^{2}b^{2}\left(a^{2}\right)^{2}}{-\frac{1}{2}ba^{2}}$$

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

$$\frac{-9\times \left(\frac{1}{3}\right)^{2}b^{2}a^{4}}{-\frac{1}{2}ba^{2}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{-9\times \frac{1}{9}b^{2}a^{4}}{-\frac{1}{2}ba^{2}}$$

Multiply -9 and \frac{1}{9} to get -1.

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

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

$$\frac{-ba^{2}}{-\frac{1}{2}}$$

Divide -ba^{2} by -\frac{1}{2} by multiplying -ba^{2} by the reciprocal of -\frac{1}{2}.

$$\frac{-ba^{2}\times 2}{-1}$$

Cancel out -1 and -1.

$$ba^{2}\times 2$$