Solve {left(frac{3{x}^{5/3}{y}^{3/4}{z}^{3/2}}{4{x}^frac{2{3}}{y}^frac{1{4}}{z}^frac{5{2}}}right)}^2

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

Evaluate

$$\frac{9\times \left(\frac{x}{z}\right)^{2}y}{16}$$

Short Solution Steps

Cancel out \sqrt[4]{y}x^{\frac{2}{3}}z^{\frac{3}{2}} in both numerator and denominator.

$$\left(\frac{3\sqrt{y}x}{4z}\right)^{2}$$

To raise \frac{3\sqrt{y}x}{4z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3\sqrt{y}x\right)^{2}}{\left(4z\right)^{2}}$$

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

$$\frac{3^{2}\left(\sqrt{y}\right)^{2}x^{2}}{\left(4z\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9\left(\sqrt{y}\right)^{2}x^{2}}{\left(4z\right)^{2}}$$

Calculate \sqrt{y} to the power of 2 and get y.

$$\frac{9yx^{2}}{\left(4z\right)^{2}}$$

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

$$\frac{9yx^{2}}{4^{2}z^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9yx^{2}}{16z^{2}}$$

Expand

$$\frac{9\times \left(\frac{x}{z}\right)^{2}y}{16}$$

Short Solution Steps

Cancel out \sqrt[4]{y}x^{\frac{2}{3}}z^{\frac{3}{2}} in both numerator and denominator.

$$\left(\frac{3\sqrt{y}x}{4z}\right)^{2}$$

To raise \frac{3\sqrt{y}x}{4z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3\sqrt{y}x\right)^{2}}{\left(4z\right)^{2}}$$

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

$$\frac{3^{2}\left(\sqrt{y}\right)^{2}x^{2}}{\left(4z\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9\left(\sqrt{y}\right)^{2}x^{2}}{\left(4z\right)^{2}}$$

Calculate \sqrt{y} to the power of 2 and get y.

$$\frac{9yx^{2}}{\left(4z\right)^{2}}$$

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

$$\frac{9yx^{2}}{4^{2}z^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9yx^{2}}{16z^{2}}$$