Rules of Exponents

Evaluate \[ \Large 3^{2^3}. \]

Evaluate

\[ \huge 4^{3^{2^{1^{0}}}}. \]

\[ \Large P = \frac{4^{3^2}}{2^{3^4}} \]

Which of the following is correct about the above number \(P?\)

\[ P < 10^{-10} \] \[ 10^{-10} < P < 10^{-5} \] \[ 10^{-5} < P < 1 \] \[ 1 < P < 10^5 \] \[ 10^5 < P < 10^{10} \] \[ 10^{10} < P \]

\[ \Huge 2^{2^{2^{2^2}}} \qquad 3^{3^{3^3}} \qquad 10^{10^{10}} \]

Which of the above is the largest?

\[ \Large 10^{10^{10}} \]

How many digits does the above number have?

Rules of Exponents - Tower Rule