Solve (-25/9x^3y^2z):(-10/3xy^2z)*(6xy)^2

$$( - \frac { 25 } { 9 } x ^ { 3 } y ^ { 2 } z ) : ( - \frac { 10 } { 3 } x y ^ { 2 } z ) \cdot ( 6 x y ) ^ { 2 }$$

Evaluate

$$30y^{2}x^{4}$$

Solution Steps

Cancel out xzy^{2} in both numerator and denominator.

$$\frac{-\frac{25}{9}x^{2}}{-\frac{10}{3}}\times \left(6xy\right)^{2}$$

Divide -\frac{25}{9}x^{2} by -\frac{10}{3} by multiplying -\frac{25}{9}x^{2} by the reciprocal of -\frac{10}{3}.

$$\frac{-\frac{25}{9}x^{2}\times 3}{-10}\times \left(6xy\right)^{2}$$

Multiply -\frac{25}{9} and 3 to get -\frac{25}{3}.

$$\frac{-\frac{25}{3}x^{2}}{-10}\times \left(6xy\right)^{2}$$

Divide -\frac{25}{3}x^{2} by -10 to get \frac{5}{6}x^{2}.

$$\frac{5}{6}x^{2}\times \left(6xy\right)^{2}$$

Expand \left(6xy\right)^{2}.

$$\frac{5}{6}x^{2}\times 6^{2}x^{2}y^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{5}{6}x^{2}\times 36x^{2}y^{2}$$

Multiply \frac{5}{6} and 36 to get 30.

$$30x^{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$30x^{4}y^{2}$$

Expand

$$30y^{2}x^{4}$$

Solution Steps

Cancel out xzy^{2} in both numerator and denominator.

$$\frac{-\frac{25}{9}x^{2}}{-\frac{10}{3}}\times \left(6xy\right)^{2}$$

Divide -\frac{25}{9}x^{2} by -\frac{10}{3} by multiplying -\frac{25}{9}x^{2} by the reciprocal of -\frac{10}{3}.

$$\frac{-\frac{25}{9}x^{2}\times 3}{-10}\times \left(6xy\right)^{2}$$

Multiply -\frac{25}{9} and 3 to get -\frac{25}{3}.

$$\frac{-\frac{25}{3}x^{2}}{-10}\times \left(6xy\right)^{2}$$

Divide -\frac{25}{3}x^{2} by -10 to get \frac{5}{6}x^{2}.

$$\frac{5}{6}x^{2}\times \left(6xy\right)^{2}$$

Expand \left(6xy\right)^{2}.

$$\frac{5}{6}x^{2}\times 6^{2}x^{2}y^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{5}{6}x^{2}\times 36x^{2}y^{2}$$

Multiply \frac{5}{6} and 36 to get 30.

$$30x^{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$30x^{4}y^{2}$$