Solve (23/3*2^7/1^12sqrt{2})^2

$$( \frac { 2 \frac { 3 } { 3 } \cdot 2 ^ { 7 } } { 1 ^ { 12 } \sqrt { 2 } } ) ^ { 2 }$$

Evaluate

$$73728$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\left(\frac{\frac{6+3}{3}\times 2^{7}}{1^{12}\sqrt{2}}\right)^{2}$$

Add 6 and 3 to get 9.

$$\left(\frac{\frac{9}{3}\times 2^{7}}{1^{12}\sqrt{2}}\right)^{2}$$

Divide 9 by 3 to get 3.

$$\left(\frac{3\times 2^{7}}{1^{12}\sqrt{2}}\right)^{2}$$

Calculate 2 to the power of 7 and get 128.

$$\left(\frac{3\times 128}{1^{12}\sqrt{2}}\right)^{2}$$

Multiply 3 and 128 to get 384.

$$\left(\frac{384}{1^{12}\sqrt{2}}\right)^{2}$$

Calculate 1 to the power of 12 and get 1.

$$\left(\frac{384}{1\sqrt{2}}\right)^{2}$$

Rationalize the denominator of \frac{384}{1\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\left(\frac{384\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}$$

The square of \sqrt{2} is 2.

$$\left(\frac{384\sqrt{2}}{2}\right)^{2}$$

Divide 384\sqrt{2} by 2 to get 192\sqrt{2}.

$$\left(192\sqrt{2}\right)^{2}$$

Expand \left(192\sqrt{2}\right)^{2}.

$$192^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 192 to the power of 2 and get 36864.

$$36864\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$36864\times 2$$

Multiply 36864 and 2 to get 73728.

$$73728$$

Factor

$$2^{13}\times 3^{2}$$