Solve left(left(left(22^2right)^2right)^2right)^2

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

Evaluate

$$16777216$$

Solution Steps

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

$$\left(\left(\left(2^{3}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(\left(2^{6}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(2^{12}\right)^{2}$$

Calculate 2 to the power of 12 and get 4096.

$$4096^{2}$$

Calculate 4096 to the power of 2 and get 16777216.

$$16777216$$

Factor

$$2^{24}$$