Solve sqrt{(-2^{-2})^-2*(2(2^2))+2^2^2}

$$\sqrt { ( - 2 ^ { - 2 } ) ^ { - 2 } \times ( 2 ( 2 ^ { 2 } ) ) + 2 ^ { 2 ^ { 2 } } }$$

Evaluate

$$12$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\sqrt{\left(-2^{-2}\right)^{-2}\times 2^{3}+2^{2^{2}}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\sqrt{\left(-\frac{1}{4}\right)^{-2}\times 2^{3}+2^{2^{2}}}$$

Calculate -\frac{1}{4} to the power of -2 and get 16.

$$\sqrt{16\times 2^{3}+2^{2^{2}}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{16\times 8+2^{2^{2}}}$$

Multiply 16 and 8 to get 128.

$$\sqrt{128+2^{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{128+2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{128+16}$$

Add 128 and 16 to get 144.

$$\sqrt{144}$$

Calculate the square root of 144 and get 12.

$$12$$

Factor

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