Solve (3/5x^{4}y^{3}z^{3}+1/4x^{4}y^{3}z^{3}-3/8x^4y^3z^3):(2/5xyz+frac{3}{2}xyz-xyz)+(frac{7}{10}x^2yz)*(frac{10}{7}xyz)

$$( \frac { 3 } { 5 } x ^ { 4 } y ^ { 3 } z ^ { 3 } + \frac { 1 } { 4 } x ^ { 4 } y ^ { 3 } z ^ { 3 } - \frac { 3 } { 8 } x ^ { 4 } y ^ { 3 } z ^ { 3 } ) : ( \frac { 2 } { 5 } x y z + \frac { 3 } { 2 } x y z - x y z ) + ( \frac { 7 } { 10 } x ^ { 2 } y z ) \cdot ( \frac { 10 } { 7 } x y z )$$

Evaluate

$$\frac{55x^{3}\left(yz\right)^{2}}{36}$$

Solution Steps

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}yz\times \frac{10}{7}yz$$

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z\times \frac{10}{7}z$$

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{3}{5}x^{4}y^{3}z^{3} and \frac{1}{4}x^{4}y^{3}z^{3} to get \frac{17}{20}x^{4}y^{3}z^{3}.

$$\frac{\frac{17}{20}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{17}{20}x^{4}y^{3}z^{3} and -\frac{3}{8}x^{4}y^{3}z^{3} to get \frac{19}{40}x^{4}y^{3}z^{3}.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{2}{5}xyz and \frac{3}{2}xyz to get \frac{19}{10}xyz.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{19}{10}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{19}{10}xyz and -xyz to get \frac{9}{10}xyz.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{9}{10}xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Cancel out xyz in both numerator and denominator.

$$\frac{\frac{19}{40}y^{2}z^{2}x^{3}}{\frac{9}{10}}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Divide \frac{19}{40}y^{2}z^{2}x^{3} by \frac{9}{10} by multiplying \frac{19}{40}y^{2}z^{2}x^{3} by the reciprocal of \frac{9}{10}.

$$\frac{\frac{19}{40}y^{2}z^{2}x^{3}\times 10}{9}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Multiply \frac{19}{40} and 10 to get \frac{19}{4}.

$$\frac{\frac{19}{4}y^{2}z^{2}x^{3}}{9}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Divide \frac{19}{4}y^{2}z^{2}x^{3} by 9 to get \frac{19}{36}y^{2}z^{2}x^{3}.

$$\frac{19}{36}y^{2}z^{2}x^{3}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Multiply \frac{7}{10} and \frac{10}{7} to get 1.

$$\frac{19}{36}y^{2}z^{2}x^{3}+x^{3}y^{2}z^{2}$$

Combine \frac{19}{36}y^{2}z^{2}x^{3} and x^{3}y^{2}z^{2} to get \frac{55}{36}y^{2}z^{2}x^{3}.

$$\frac{55}{36}y^{2}z^{2}x^{3}$$

Expand

$$\frac{55x^{3}\left(yz\right)^{2}}{36}$$

Solution Steps

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}yz\times \frac{10}{7}yz$$

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z\times \frac{10}{7}z$$

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

$$\frac{\frac{3}{5}x^{4}y^{3}z^{3}+\frac{1}{4}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{3}{5}x^{4}y^{3}z^{3} and \frac{1}{4}x^{4}y^{3}z^{3} to get \frac{17}{20}x^{4}y^{3}z^{3}.

$$\frac{\frac{17}{20}x^{4}y^{3}z^{3}-\frac{3}{8}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{17}{20}x^{4}y^{3}z^{3} and -\frac{3}{8}x^{4}y^{3}z^{3} to get \frac{19}{40}x^{4}y^{3}z^{3}.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{2}{5}xyz+\frac{3}{2}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{2}{5}xyz and \frac{3}{2}xyz to get \frac{19}{10}xyz.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{19}{10}xyz-xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Combine \frac{19}{10}xyz and -xyz to get \frac{9}{10}xyz.

$$\frac{\frac{19}{40}x^{4}y^{3}z^{3}}{\frac{9}{10}xyz}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Cancel out xyz in both numerator and denominator.

$$\frac{\frac{19}{40}y^{2}z^{2}x^{3}}{\frac{9}{10}}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Divide \frac{19}{40}y^{2}z^{2}x^{3} by \frac{9}{10} by multiplying \frac{19}{40}y^{2}z^{2}x^{3} by the reciprocal of \frac{9}{10}.

$$\frac{\frac{19}{40}y^{2}z^{2}x^{3}\times 10}{9}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Multiply \frac{19}{40} and 10 to get \frac{19}{4}.

$$\frac{\frac{19}{4}y^{2}z^{2}x^{3}}{9}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Divide \frac{19}{4}y^{2}z^{2}x^{3} by 9 to get \frac{19}{36}y^{2}z^{2}x^{3}.

$$\frac{19}{36}y^{2}z^{2}x^{3}+\frac{7}{10}x^{3}y^{2}z^{2}\times \frac{10}{7}$$

Multiply \frac{7}{10} and \frac{10}{7} to get 1.

$$\frac{19}{36}y^{2}z^{2}x^{3}+x^{3}y^{2}z^{2}$$

Combine \frac{19}{36}y^{2}z^{2}x^{3} and x^{3}y^{2}z^{2} to get \frac{55}{36}y^{2}z^{2}x^{3}.

$$\frac{55}{36}y^{2}z^{2}x^{3}$$