Despite the other answer, this looks like exponentiation.
The parentheses are necessary; without them
[tex]4^{3^5}=4^{(3^5)}[/tex]
which happens to be 147 digits long.
We're asked
[tex](4^3)^5[/tex]
Parenthesized this way we can multiply the exponents
[tex](4^3)^5 = 4^{15}=(2^2)^{15}=2^{30}[/tex]
Two to the thirtieth is 1,073,741,824, about a billion. But that's not really that helpful for understanding what's going on so let's leave it as a power of two.
Answer: [tex]2^{30}[/tex]
