Solve {-5[9x^{6}y^{2}:(3x^{3}y)-3x^{3}y+9x^{2}y:(9xy)]^2+5x^2}^3+(4xy)^2:(-4xy)

$$\{ - 5 [ 9 x ^ { 6 } y ^ { 2 } : ( 3 x ^ { 3 } y ) - 3 x ^ { 3 } y + 9 x ^ { 2 } y : ( 9 x y ) ] ^ { 2 } + 5 x ^ { 2 } \} ^ { 3 } + ( 4 x y ) ^ { 2 } : ( - 4 x y )$$

Evaluate

$$-4xy$$

Solution Steps

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

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

Combine 3yx^{3} and -3x^{3}y to get 0.

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

Cancel out 9xy in both numerator and denominator.

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

Combine -5x^{2} and 5x^{2} to get 0.

$$0^{3}+\frac{\left(4xy\right)^{2}}{-4xy}$$

Calculate 0 to the power of 3 and get 0.

$$0+\frac{\left(4xy\right)^{2}}{-4xy}$$

Expand \left(4xy\right)^{2}.

$$0+\frac{4^{2}x^{2}y^{2}}{-4xy}$$

Calculate 4 to the power of 2 and get 16.

$$0+\frac{16x^{2}y^{2}}{-4xy}$$

Cancel out 4xy in both numerator and denominator.

$$0+\frac{4xy}{-1}$$

Anything divided by -1 gives its opposite.

$$0-4xy$$

Anything plus zero gives itself.

$$-4xy$$

Expand

$$-4xy$$

Solution Steps

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

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

Combine 3yx^{3} and -3x^{3}y to get 0.

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

Cancel out 9xy in both numerator and denominator.

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

Combine -5x^{2} and 5x^{2} to get 0.

$$0^{3}+\frac{\left(4xy\right)^{2}}{-4xy}$$

Calculate 0 to the power of 3 and get 0.

$$0+\frac{\left(4xy\right)^{2}}{-4xy}$$

Expand \left(4xy\right)^{2}.

$$0+\frac{4^{2}x^{2}y^{2}}{-4xy}$$

Calculate 4 to the power of 2 and get 16.

$$0+\frac{16x^{2}y^{2}}{-4xy}$$

Cancel out 4xy in both numerator and denominator.

$$0+\frac{4xy}{-1}$$

Anything divided by -1 gives its opposite.

$$0-4xy$$

Anything plus zero gives itself.

$$-4xy$$