Solve [(3/10x)(-5xy^3)+(2/7x^3y^3):(-4/7x)]:(-xy)+1/5x(5y)^2

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

Evaluate

$$7xy^{2}$$

Short Solution Steps

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

$$\frac{\frac{3}{10}x^{2}\left(-5\right)y^{3}+\frac{\frac{2}{7}x^{3}y^{3}}{-\frac{4}{7}x}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Multiply \frac{3}{10} and -5 to get -\frac{3}{2}.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{3}y^{3}}{-\frac{4}{7}x}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Cancel out x in both numerator and denominator.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{2}y^{3}}{-\frac{4}{7}}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Divide \frac{2}{7}x^{2}y^{3} by -\frac{4}{7} by multiplying \frac{2}{7}x^{2}y^{3} by the reciprocal of -\frac{4}{7}.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{2}y^{3}\times 7}{-4}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Multiply \frac{2}{7} and 7 to get 2.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{2x^{2}y^{3}}{-4}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Divide 2x^{2}y^{3} by -4 to get -\frac{1}{2}x^{2}y^{3}.

$$\frac{-\frac{3}{2}x^{2}y^{3}-\frac{1}{2}x^{2}y^{3}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

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

$$\frac{-2x^{2}y^{3}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Cancel out y in both numerator and denominator.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Expand \left(5y\right)^{2}.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times 5^{2}y^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times 25y^{2}$$

Multiply \frac{1}{5} and 25 to get 5.

$$\frac{-2x^{2}y^{2}}{-x}+5xy^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5xy^{2} times \frac{-x}{-x}.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{5xy^{2}\left(-1\right)x}{-x}$$

Since \frac{-2x^{2}y^{2}}{-x} and \frac{5xy^{2}\left(-1\right)x}{-x} have the same denominator, add them by adding their numerators.

$$\frac{-2x^{2}y^{2}+5xy^{2}\left(-1\right)x}{-x}$$

Do the multiplications in -2x^{2}y^{2}+5xy^{2}\left(-1\right)x.

$$\frac{-2x^{2}y^{2}-5x^{2}y^{2}}{-x}$$

Combine like terms in -2x^{2}y^{2}-5x^{2}y^{2}.

$$\frac{-7x^{2}y^{2}}{-x}$$

Cancel out x in both numerator and denominator.

$$\frac{-7xy^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$7xy^{2}$$

Expand

$$7xy^{2}$$

Short Solution Steps

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

$$\frac{\frac{3}{10}x^{2}\left(-5\right)y^{3}+\frac{\frac{2}{7}x^{3}y^{3}}{-\frac{4}{7}x}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Multiply \frac{3}{10} and -5 to get -\frac{3}{2}.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{3}y^{3}}{-\frac{4}{7}x}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Cancel out x in both numerator and denominator.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{2}y^{3}}{-\frac{4}{7}}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Divide \frac{2}{7}x^{2}y^{3} by -\frac{4}{7} by multiplying \frac{2}{7}x^{2}y^{3} by the reciprocal of -\frac{4}{7}.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{\frac{2}{7}x^{2}y^{3}\times 7}{-4}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Multiply \frac{2}{7} and 7 to get 2.

$$\frac{-\frac{3}{2}x^{2}y^{3}+\frac{2x^{2}y^{3}}{-4}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Divide 2x^{2}y^{3} by -4 to get -\frac{1}{2}x^{2}y^{3}.

$$\frac{-\frac{3}{2}x^{2}y^{3}-\frac{1}{2}x^{2}y^{3}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

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

$$\frac{-2x^{2}y^{3}}{\left(-x\right)y}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Cancel out y in both numerator and denominator.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times \left(5y\right)^{2}$$

Expand \left(5y\right)^{2}.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times 5^{2}y^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{1}{5}x\times 25y^{2}$$

Multiply \frac{1}{5} and 25 to get 5.

$$\frac{-2x^{2}y^{2}}{-x}+5xy^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5xy^{2} times \frac{-x}{-x}.

$$\frac{-2x^{2}y^{2}}{-x}+\frac{5xy^{2}\left(-1\right)x}{-x}$$

Since \frac{-2x^{2}y^{2}}{-x} and \frac{5xy^{2}\left(-1\right)x}{-x} have the same denominator, add them by adding their numerators.

$$\frac{-2x^{2}y^{2}+5xy^{2}\left(-1\right)x}{-x}$$

Do the multiplications in -2x^{2}y^{2}+5xy^{2}\left(-1\right)x.

$$\frac{-2x^{2}y^{2}-5x^{2}y^{2}}{-x}$$

Combine like terms in -2x^{2}y^{2}-5x^{2}y^{2}.

$$\frac{-7x^{2}y^{2}}{-x}$$

Cancel out x in both numerator and denominator.

$$\frac{-7xy^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$7xy^{2}$$