Solve [-3/2xy^{2}*(1/9x^{4}y^{3})-3/5x^{3}y(-5/6x^2y^4)]:(frac{8}{6}x^4y^4)-frac{1}{3}xy

$$[ - \frac { 3 } { 2 } x y ^ { 2 } \cdot ( \frac { 1 } { 9 } x ^ { 4 } y ^ { 3 } ) - \frac { 3 } { 5 } x ^ { 3 } y ( - \frac { 5 } { 6 } x ^ { 2 } y ^ { 4 } ) ] : ( \frac { 8 } { 6 } x ^ { 4 } y ^ { 4 } ) - \frac { 1 } { 3 } x y$$

Evaluate

$$-\frac{xy}{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{2}\times \frac{1}{9}y^{3}-\frac{3}{5}x^{3}y\left(-\frac{5}{6}\right)x^{2}y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{3}y\left(-\frac{5}{6}\right)x^{2}y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{5}y\left(-\frac{5}{6}\right)y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{5}y^{5}\left(-\frac{5}{6}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Multiply -\frac{3}{2} and \frac{1}{9} to get -\frac{1}{6}.

$$\frac{-\frac{1}{6}x^{5}y^{5}-\frac{3}{5}x^{5}y^{5}\left(-\frac{5}{6}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Multiply \frac{3}{5} and -\frac{5}{6} to get -\frac{1}{2}.

$$\frac{-\frac{1}{6}x^{5}y^{5}-\left(-\frac{1}{2}x^{5}y^{5}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

The opposite of -\frac{1}{2}x^{5}y^{5} is \frac{1}{2}x^{5}y^{5}.

$$\frac{-\frac{1}{6}x^{5}y^{5}+\frac{1}{2}x^{5}y^{5}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Combine -\frac{1}{6}x^{5}y^{5} and \frac{1}{2}x^{5}y^{5} to get \frac{1}{3}x^{5}y^{5}.

$$\frac{\frac{1}{3}x^{5}y^{5}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}x^{5}y^{5}}{\frac{4}{3}x^{4}y^{4}}-\frac{1}{3}xy$$

Cancel out x^{4}y^{4} in both numerator and denominator.

$$\frac{\frac{1}{3}xy}{\frac{4}{3}}-\frac{1}{3}xy$$

Divide \frac{1}{3}xy by \frac{4}{3} by multiplying \frac{1}{3}xy by the reciprocal of \frac{4}{3}.

$$\frac{\frac{1}{3}xy\times 3}{4}-\frac{1}{3}xy$$

Multiply \frac{1}{3} and 3 to get 1.

$$\frac{xy}{4}-\frac{1}{3}xy$$

Combine \frac{xy}{4} and -\frac{1}{3}xy to get -\frac{1}{12}xy.

$$-\frac{1}{12}xy$$

Expand

$$-\frac{xy}{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{2}\times \frac{1}{9}y^{3}-\frac{3}{5}x^{3}y\left(-\frac{5}{6}\right)x^{2}y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{3}y\left(-\frac{5}{6}\right)x^{2}y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{5}y\left(-\frac{5}{6}\right)y^{4}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{-\frac{3}{2}x^{5}y^{5}\times \frac{1}{9}-\frac{3}{5}x^{5}y^{5}\left(-\frac{5}{6}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Multiply -\frac{3}{2} and \frac{1}{9} to get -\frac{1}{6}.

$$\frac{-\frac{1}{6}x^{5}y^{5}-\frac{3}{5}x^{5}y^{5}\left(-\frac{5}{6}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Multiply \frac{3}{5} and -\frac{5}{6} to get -\frac{1}{2}.

$$\frac{-\frac{1}{6}x^{5}y^{5}-\left(-\frac{1}{2}x^{5}y^{5}\right)}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

The opposite of -\frac{1}{2}x^{5}y^{5} is \frac{1}{2}x^{5}y^{5}.

$$\frac{-\frac{1}{6}x^{5}y^{5}+\frac{1}{2}x^{5}y^{5}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Combine -\frac{1}{6}x^{5}y^{5} and \frac{1}{2}x^{5}y^{5} to get \frac{1}{3}x^{5}y^{5}.

$$\frac{\frac{1}{3}x^{5}y^{5}}{\frac{8}{6}x^{4}y^{4}}-\frac{1}{3}xy$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}x^{5}y^{5}}{\frac{4}{3}x^{4}y^{4}}-\frac{1}{3}xy$$

Cancel out x^{4}y^{4} in both numerator and denominator.

$$\frac{\frac{1}{3}xy}{\frac{4}{3}}-\frac{1}{3}xy$$

Divide \frac{1}{3}xy by \frac{4}{3} by multiplying \frac{1}{3}xy by the reciprocal of \frac{4}{3}.

$$\frac{\frac{1}{3}xy\times 3}{4}-\frac{1}{3}xy$$

Multiply \frac{1}{3} and 3 to get 1.

$$\frac{xy}{4}-\frac{1}{3}xy$$

Combine \frac{xy}{4} and -\frac{1}{3}xy to get -\frac{1}{12}xy.

$$-\frac{1}{12}xy$$