Solve Z-3/10+[45/28xy*(-49/75xy^{3})-(-13/9x^4y^5):(frac{65}{6}x^2y)]:(-frac{55}{8}x^2)

$$Z - \frac { 3 } { 10 } + [ \frac { 45 } { 28 } x y \cdot ( - \frac { 49 } { 75 } x y ^ { 3 } ) - ( - \frac { 13 } { 9 } x ^ { 4 } y ^ { 5 } ) : ( \frac { 65 } { 6 } x ^ { 2 } y ) ] : ( - \frac { 55 } { 8 } x ^ { 2 } )$$

Evaluate

$$\frac{2y^{4}}{15}+Z-\frac{3}{10}$$

Solution Steps

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

$$Z-\frac{3}{10}+\frac{\frac{45}{28}x^{2}y\left(-\frac{49}{75}\right)y^{3}-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$Z-\frac{3}{10}+\frac{\frac{45}{28}x^{2}y^{4}\left(-\frac{49}{75}\right)-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

Multiply \frac{45}{28} and -\frac{49}{75} to get -\frac{21}{20}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

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

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{2}y^{4}}{\frac{65}{6}}}{-\frac{55}{8}x^{2}}$$

Divide -\frac{13}{9}x^{2}y^{4} by \frac{65}{6} by multiplying -\frac{13}{9}x^{2}y^{4} by the reciprocal of \frac{65}{6}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{2}y^{4}\times 6}{65}}{-\frac{55}{8}x^{2}}$$

Multiply -\frac{13}{9} and 6 to get -\frac{26}{3}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{26}{3}x^{2}y^{4}}{65}}{-\frac{55}{8}x^{2}}$$

Divide -\frac{26}{3}x^{2}y^{4} by 65 to get -\frac{2}{15}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\left(-\frac{2}{15}x^{2}y^{4}\right)}{-\frac{55}{8}x^{2}}$$

The opposite of -\frac{2}{15}x^{2}y^{4} is \frac{2}{15}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}+\frac{2}{15}x^{2}y^{4}}{-\frac{55}{8}x^{2}}$$

Combine -\frac{21}{20}x^{2}y^{4} and \frac{2}{15}x^{2}y^{4} to get -\frac{11}{12}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}x^{2}y^{4}}{-\frac{55}{8}x^{2}}$$

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

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}y^{4}}{-\frac{55}{8}}$$

Divide -\frac{11}{12}y^{4} by -\frac{55}{8} by multiplying -\frac{11}{12}y^{4} by the reciprocal of -\frac{55}{8}.

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}y^{4}\times 8}{-55}$$

Multiply -\frac{11}{12} and 8 to get -\frac{22}{3}.

$$Z-\frac{3}{10}+\frac{-\frac{22}{3}y^{4}}{-55}$$

Divide -\frac{22}{3}y^{4} by -55 to get \frac{2}{15}y^{4}.

$$Z-\frac{3}{10}+\frac{2}{15}y^{4}$$

Expand

$$\frac{2y^{4}}{15}+Z-\frac{3}{10}$$

Solution Steps

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

$$Z-\frac{3}{10}+\frac{\frac{45}{28}x^{2}y\left(-\frac{49}{75}\right)y^{3}-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$Z-\frac{3}{10}+\frac{\frac{45}{28}x^{2}y^{4}\left(-\frac{49}{75}\right)-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

Multiply \frac{45}{28} and -\frac{49}{75} to get -\frac{21}{20}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{4}y^{5}}{\frac{65}{6}x^{2}y}}{-\frac{55}{8}x^{2}}$$

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

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{2}y^{4}}{\frac{65}{6}}}{-\frac{55}{8}x^{2}}$$

Divide -\frac{13}{9}x^{2}y^{4} by \frac{65}{6} by multiplying -\frac{13}{9}x^{2}y^{4} by the reciprocal of \frac{65}{6}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{13}{9}x^{2}y^{4}\times 6}{65}}{-\frac{55}{8}x^{2}}$$

Multiply -\frac{13}{9} and 6 to get -\frac{26}{3}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\frac{-\frac{26}{3}x^{2}y^{4}}{65}}{-\frac{55}{8}x^{2}}$$

Divide -\frac{26}{3}x^{2}y^{4} by 65 to get -\frac{2}{15}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}-\left(-\frac{2}{15}x^{2}y^{4}\right)}{-\frac{55}{8}x^{2}}$$

The opposite of -\frac{2}{15}x^{2}y^{4} is \frac{2}{15}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{21}{20}x^{2}y^{4}+\frac{2}{15}x^{2}y^{4}}{-\frac{55}{8}x^{2}}$$

Combine -\frac{21}{20}x^{2}y^{4} and \frac{2}{15}x^{2}y^{4} to get -\frac{11}{12}x^{2}y^{4}.

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}x^{2}y^{4}}{-\frac{55}{8}x^{2}}$$

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

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}y^{4}}{-\frac{55}{8}}$$

Divide -\frac{11}{12}y^{4} by -\frac{55}{8} by multiplying -\frac{11}{12}y^{4} by the reciprocal of -\frac{55}{8}.

$$Z-\frac{3}{10}+\frac{-\frac{11}{12}y^{4}\times 8}{-55}$$

Multiply -\frac{11}{12} and 8 to get -\frac{22}{3}.

$$Z-\frac{3}{10}+\frac{-\frac{22}{3}y^{4}}{-55}$$

Divide -\frac{22}{3}y^{4} by -55 to get \frac{2}{15}y^{4}.

$$Z-\frac{3}{10}+\frac{2}{15}y^{4}$$