Exponent - \[(((x^{y})^{z})^{w})^{k} \] is indices where x, ,y ,z,w,k all must be real numbers.
Boundary condition- All of these numbers should be taken in such a way that it should not result a complex no
like x= -1 and y=0.5 and z,w,k would be any other real value
Steps to solve
It sshould be evaluated from innermost parenthesis onwards.
For example \[(2^{3})^{4}=4096 \]
\[((2)^{3})^{2}=64 \]
Exponent of the form \[a^{b^{c}} \] should be evaluated from the outermost power and should be solved towards innermost numbers
\[2^{3^{2^{2}}}=2^{81} \neq 2^{12} \]
In this case first 22 which is 4, has been evaluated then 34 which comes to 81 is evaluated then we get 281
Similarly \[5^{2^{4}}=5^{16} \]
\[4^{2^{2^{2^{2}}}}=4^{65536} \]
Law of exponent
\[(ab)^{m}=a^{m}*b^{m} \]
For example
\[(4*3)^{5}=4^{5}*3^{5}=12^{5} \]
\[6^{3}*7^{3}=42^{3} \]
