Solve (sqrt{14}*4)^2(sqrt{14}*-4)^2

$$( \sqrt { 14 } \times 4 ) ^ { 2 } ( \sqrt { 14 } \times - 4 ) ^ { 2 }$$

Evaluate

$$50176$$

Solution Steps

Expand \left(4\sqrt{14}\right)^{2}.

$$4^{2}\left(\sqrt{14}\right)^{2}\left(\sqrt{14}\left(-4\right)\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{14}\right)^{2}\left(\sqrt{14}\left(-4\right)\right)^{2}$$

The square of \sqrt{14} is 14.

$$16\times 14\left(\sqrt{14}\left(-4\right)\right)^{2}$$

Multiply 16 and 14 to get 224.

$$224\left(\sqrt{14}\left(-4\right)\right)^{2}$$

Expand \left(\sqrt{14}\left(-4\right)\right)^{2}.

$$224\left(\sqrt{14}\right)^{2}\left(-4\right)^{2}$$

The square of \sqrt{14} is 14.

$$224\times 14\left(-4\right)^{2}$$

Calculate -4 to the power of 2 and get 16.

$$224\times 14\times 16$$

Multiply 14 and 16 to get 224.

$$224\times 224$$

Multiply 224 and 224 to get 50176.

$$50176$$

Factor

$$2^{10}\times 7^{2}$$