求解 {left({left({left({left({left({left(left(left(left(2^2right)^2right)^2right)^2right)}^{2}right)}^{2}right)}^2right)}^2right)}^2right)}^2

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

求值

$$179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216$$

求解步骤

要对幂进行幂运算，即将指数相乘。2 乘 2 得 4。

$$\left(\left(\left(\left(\left(\left(\left(\left(2^{4}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。4 乘 2 得 8。

$$\left(\left(\left(\left(\left(\left(\left(2^{8}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。8 乘 2 得 16。

$$\left(\left(\left(\left(\left(\left(2^{16}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。16 乘 2 得 32。

$$\left(\left(\left(\left(\left(2^{32}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。32 乘 2 得 64。

$$\left(\left(\left(\left(2^{64}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。64 乘 2 得 128。

$$\left(\left(\left(2^{128}\right)^{2}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。128 乘 2 得 256。

$$\left(\left(2^{256}\right)^{2}\right)^{2}$$

要对幂进行幂运算，即将指数相乘。256 乘 2 得 512。

$$\left(2^{512}\right)^{2}$$

计算 512 的 2 乘方，得到 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096。

$$13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096^{2}$$

计算 2 的 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 乘方，得到 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216。

$$179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216$$

因式分解

$$2^{1024}$$