Solve 5255222%8/2{{left({left(2frac{2/frac{{}/}right)}^2right)}^2}}

$$5255222 \% \frac{ 8 }{ \frac{ 2 }{ { \left( { \left(2 \frac{ 2 }{ \frac{ }{ } \frac { } { } } \right) }^{ 2 } \right) }^{ 2 } } }$$

Evaluate

$$54$$

Solution Steps

Divide 1 by 1 to get 1.

$$5255222\text{bmod}\left(\frac{8}{\frac{2}{\left(\left(2\times \frac{2}{1\times \frac{1}{1}}\right)^{2}\right)^{2}}}\right)$$

Divide 1 by 1 to get 1.

$$5255222\text{bmod}\left(\frac{8}{\frac{2}{\left(\left(2\times \frac{2}{1\times 1}\right)^{2}\right)^{2}}}\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$5255222\text{bmod}\left(\frac{8}{\frac{2}{\left(2\times \frac{2}{1\times 1}\right)^{4}}}\right)$$

Divide 8 by \frac{2}{\left(2\times \frac{2}{1\times 1}\right)^{4}} by multiplying 8 by the reciprocal of \frac{2}{\left(2\times \frac{2}{1\times 1}\right)^{4}}.

$$5255222\text{bmod}\left(\frac{8\times \left(2\times \frac{2}{1\times 1}\right)^{4}}{2}\right)$$

Multiply 1 and 1 to get 1.

$$5255222\text{bmod}\left(\frac{8\times \left(2\times \frac{2}{1}\right)^{4}}{2}\right)$$

Anything divided by one gives itself.

$$5255222\text{bmod}\left(\frac{8\times \left(2\times 2\right)^{4}}{2}\right)$$

Multiply 2 and 2 to get 4.

$$5255222\text{bmod}\left(\frac{8\times 4^{4}}{2}\right)$$

Calculate 4 to the power of 4 and get 256.

$$5255222\text{bmod}\left(\frac{8\times 256}{2}\right)$$

Multiply 8 and 256 to get 2048.

$$5255222\text{bmod}\left(\frac{2048}{2}\right)$$

Divide 2048 by 2 to get 1024.

$$5255222\text{bmod}1024$$

Divide 5255222 by 1024 to get the remainder 54.

$$54$$

Factor

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