Solve (frac{2^{2}+3^{3}+4^2}{2^4*3^2})^2

$$( \frac { 2 ^ { 2 } + 3 ^ { 3 } + 4 ^ { 2 } } { 2 ^ { 4 } * 3 ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{2209}{20736}\approx 0.106529707$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{4+3^{3}+4^{2}}{2^{4}\times 3^{2}}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{4+27+4^{2}}{2^{4}\times 3^{2}}\right)^{2}$$

Add 4 and 27 to get 31.

$$\left(\frac{31+4^{2}}{2^{4}\times 3^{2}}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{31+16}{2^{4}\times 3^{2}}\right)^{2}$$

Add 31 and 16 to get 47.

$$\left(\frac{47}{2^{4}\times 3^{2}}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\left(\frac{47}{16\times 3^{2}}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{47}{16\times 9}\right)^{2}$$

Multiply 16 and 9 to get 144.

$$\left(\frac{47}{144}\right)^{2}$$

Calculate \frac{47}{144} to the power of 2 and get \frac{2209}{20736}.

$$\frac{2209}{20736}$$

Factor

$$\frac{47 ^ {2}}{2 ^ {8} \cdot 3 ^ {4}} = 0.10652970679012345$$