Solve (3/2x^{2}y)^2*(-2xy)^3div(-3x^6y^5)

$$( \frac { 3 } { 2 } x ^ { 2 } y ) ^ { 2 } \times ( - 2 x y ) ^ { 3 } \div ( - 3 x ^ { 6 } y ^ { 5 } )$$

Evaluate

$$6x$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

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

Multiply \frac{9}{4} and -8 to get -18.

$$\frac{-18x^{4}y^{2}x^{3}y^{3}}{-3x^{6}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{-18x^{7}y^{2}y^{3}}{-3x^{6}y^{5}}$$

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

$$\frac{-18x^{7}y^{5}}{-3x^{6}y^{5}}$$

Cancel out 3y^{5}x^{6} in both numerator and denominator.

$$\frac{-6x}{-1}$$

Anything divided by -1 gives its opposite.

$$6x$$

Expand

$$6x$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

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

Multiply \frac{9}{4} and -8 to get -18.

$$\frac{-18x^{4}y^{2}x^{3}y^{3}}{-3x^{6}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{-18x^{7}y^{2}y^{3}}{-3x^{6}y^{5}}$$

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

$$\frac{-18x^{7}y^{5}}{-3x^{6}y^{5}}$$

Cancel out 3y^{5}x^{6} in both numerator and denominator.

$$\frac{-6x}{-1}$$

Anything divided by -1 gives its opposite.

$$6x$$