Solve 7x^{2}+(10/3x^{5}):(-2/3x^{3})-(-3/2x)^2:(-3/4)+(-frac{1}{2}x^2)^3:(frac{1}{32}x^5)-2x

$$7 x ^ { 2 } + ( \frac { 10 } { 3 } x ^ { 5 } ) : ( - \frac { 2 } { 3 } x ^ { 3 } ) - ( - \frac { 3 } { 2 } x ) ^ { 2 } : ( - \frac { 3 } { 4 } ) + ( - \frac { 1 } { 2 } x ^ { 2 } ) ^ { 3 } : ( \frac { 1 } { 32 } x ^ { 5 } ) - 2 x$$

Evaluate

$$x\left(5x-6\right)$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$7x^{2}+\frac{\frac{10}{3}x^{2}}{-\frac{2}{3}}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide \frac{10}{3}x^{2} by -\frac{2}{3} by multiplying \frac{10}{3}x^{2} by the reciprocal of -\frac{2}{3}.

$$7x^{2}+\frac{\frac{10}{3}x^{2}\times 3}{-2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Multiply \frac{10}{3} and 3 to get 10.

$$7x^{2}+\frac{10x^{2}}{-2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide 10x^{2} by -2 to get -5x^{2}.

$$7x^{2}-5x^{2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$2x^{2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Expand \left(-\frac{3}{2}x\right)^{2}.

$$2x^{2}-\frac{\left(-\frac{3}{2}\right)^{2}x^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$2x^{2}-\frac{\frac{9}{4}x^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide \frac{9}{4}x^{2} by -\frac{3}{4} by multiplying \frac{9}{4}x^{2} by the reciprocal of -\frac{3}{4}.

$$2x^{2}-\frac{\frac{9}{4}x^{2}\times 4}{-3}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Multiply \frac{9}{4} and 4 to get 9.

$$2x^{2}-\frac{9x^{2}}{-3}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide 9x^{2} by -3 to get -3x^{2}.

$$2x^{2}-\left(-3x^{2}\right)+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

The opposite of -3x^{2} is 3x^{2}.

$$2x^{2}+3x^{2}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

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

$$5x^{2}+\frac{\left(-\frac{1}{2}\right)^{3}\left(x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$5x^{2}+\frac{\left(-\frac{1}{2}\right)^{3}x^{6}}{\frac{1}{32}x^{5}}-2x$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$5x^{2}+\frac{-\frac{1}{8}x^{6}}{\frac{1}{32}x^{5}}-2x$$

Cancel out x^{5} in both numerator and denominator.

$$5x^{2}+\frac{-\frac{1}{8}x}{\frac{1}{32}}-2x$$

Divide -\frac{1}{8}x by \frac{1}{32} by multiplying -\frac{1}{8}x by the reciprocal of \frac{1}{32}.

$$5x^{2}-\frac{1}{8}x\times 32-2x$$

Multiply -\frac{1}{8} and 32 to get -4.

$$5x^{2}-4x-2x$$

Combine -4x and -2x to get -6x.

$$5x^{2}-6x$$

Expand

$$5x^{2}-6x$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$7x^{2}+\frac{\frac{10}{3}x^{2}}{-\frac{2}{3}}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide \frac{10}{3}x^{2} by -\frac{2}{3} by multiplying \frac{10}{3}x^{2} by the reciprocal of -\frac{2}{3}.

$$7x^{2}+\frac{\frac{10}{3}x^{2}\times 3}{-2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Multiply \frac{10}{3} and 3 to get 10.

$$7x^{2}+\frac{10x^{2}}{-2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide 10x^{2} by -2 to get -5x^{2}.

$$7x^{2}-5x^{2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$2x^{2}-\frac{\left(-\frac{3}{2}x\right)^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Expand \left(-\frac{3}{2}x\right)^{2}.

$$2x^{2}-\frac{\left(-\frac{3}{2}\right)^{2}x^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$2x^{2}-\frac{\frac{9}{4}x^{2}}{-\frac{3}{4}}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide \frac{9}{4}x^{2} by -\frac{3}{4} by multiplying \frac{9}{4}x^{2} by the reciprocal of -\frac{3}{4}.

$$2x^{2}-\frac{\frac{9}{4}x^{2}\times 4}{-3}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Multiply \frac{9}{4} and 4 to get 9.

$$2x^{2}-\frac{9x^{2}}{-3}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Divide 9x^{2} by -3 to get -3x^{2}.

$$2x^{2}-\left(-3x^{2}\right)+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

The opposite of -3x^{2} is 3x^{2}.

$$2x^{2}+3x^{2}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}+\frac{\left(-\frac{1}{2}x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

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

$$5x^{2}+\frac{\left(-\frac{1}{2}\right)^{3}\left(x^{2}\right)^{3}}{\frac{1}{32}x^{5}}-2x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$5x^{2}+\frac{\left(-\frac{1}{2}\right)^{3}x^{6}}{\frac{1}{32}x^{5}}-2x$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$5x^{2}+\frac{-\frac{1}{8}x^{6}}{\frac{1}{32}x^{5}}-2x$$

Cancel out x^{5} in both numerator and denominator.

$$5x^{2}+\frac{-\frac{1}{8}x}{\frac{1}{32}}-2x$$

Divide -\frac{1}{8}x by \frac{1}{32} by multiplying -\frac{1}{8}x by the reciprocal of \frac{1}{32}.

$$5x^{2}-\frac{1}{8}x\times 32-2x$$

Multiply -\frac{1}{8} and 32 to get -4.

$$5x^{2}-4x-2x$$

Combine -4x and -2x to get -6x.

$$5x^{2}-6x$$