Solve {left({left({left(left(left(left(9^2right)^2right)^2right)^2right)}^2right)}^2right)}^2

$${ \left( { \left( { \left( { \left( { \left( { \left( { 9 }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521$$

Solution Steps

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

$$\left(\left(\left(\left(\left(9^{4}\right)^{2}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

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

$$\left(\left(\left(\left(9^{8}\right)^{2}\right)^{2}\right)^{2}\right)^{2}$$

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

$$\left(\left(\left(9^{16}\right)^{2}\right)^{2}\right)^{2}$$

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

$$\left(\left(9^{32}\right)^{2}\right)^{2}$$

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

$$\left(9^{64}\right)^{2}$$

Calculate 9 to the power of 64 and get 11790184577738583171520872861412518665678211592275841109096961.

$$11790184577738583171520872861412518665678211592275841109096961^{2}$$

Calculate 11790184577738583171520872861412518665678211592275841109096961 to the power of 2 and get 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521$$

Factor

$$3^{256}$$