Solve {left({left({left({left(left(left(left(7^2right)^2right)^2right)^2right)}^2right)}^2right)}^2right)}^2

$${ \left( { \left( { \left( { \left( { \left( { \left( { \left( { 7 }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$2213595400046048155450188615474945937162517050260073069916366390524704974007989996848003433837940380782794455262312607598867363425940560014856027866381946458951205837379116473663246733509680721264246243189632348313601$$

Solution Steps

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

$$\left(\left(\left(\left(\left(\left(7^{4}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(\left(\left(\left(\left(7^{8}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\left(\left(\left(\left(7^{16}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 16 and 2 to get 32.

$$\left(\left(\left(7^{32}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 32 and 2 to get 64.

$$\left(\left(7^{64}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 64 and 2 to get 128.

$$\left(7^{128}\right)^{2}$$

Calculate 7 to the power of 128 and get 1487815647197611695910312681741273570332356717154798949898498305086387315423300999654757561928633305897036801.

$$1487815647197611695910312681741273570332356717154798949898498305086387315423300999654757561928633305897036801^{2}$$

Calculate 1487815647197611695910312681741273570332356717154798949898498305086387315423300999654757561928633305897036801 to the power of 2 and get 2213595400046048155450188615474945937162517050260073069916366390524704974007989996848003433837940380782794455262312607598867363425940560014856027866381946458951205837379116473663246733509680721264246243189632348313601.

$$2213595400046048155450188615474945937162517050260073069916366390524704974007989996848003433837940380782794455262312607598867363425940560014856027866381946458951205837379116473663246733509680721264246243189632348313601$$

Factor

$$7^{256}$$