Solve {left(sqrt{4^2x^2y^2z^2/{6^{2}{x}^2{y}^2{z}^2}}right)}^2

$${ \left( \sqrt{ \frac{ { 4 }^{ 2 } { x }^{ 2 } { y }^{ 2 } { z }^{ 2 } }{ { 6 }^{ 2 } { x }^{ 2 } { y }^{ 2 } { z }^{ 2 } } } \right) }^{ 2 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Cancel out x^{2}y^{2}z^{2} in both numerator and denominator.

$$\left(\sqrt{\frac{4^{2}}{6^{2}}}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\sqrt{\frac{16}{6^{2}}}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\left(\sqrt{\frac{16}{36}}\right)^{2}$$

Reduce the fraction \frac{16}{36} to lowest terms by extracting and canceling out 4.

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

The square of \sqrt{\frac{4}{9}} is \frac{4}{9}.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$