Tower of powers

Statement

Compute the resulting exponent in the tower power: $5^{(5^5)}$

Solution

In a tower of powers one starts from the top: first one computes the exponent $5^5$, then one raises $5$ to that result. $5^{(5^5)} = 5^{5\cdot 5\cdot 5\cdot 5\cdot 5} = \boxed{5^{3125}}$ Note. $5^{(5^5)}$ is enormously larger than $(5^5)^5 = 5^{25}$: without brackets the tower is evaluated from the top downwards.

Links

Topics: Numbers and operations
Concepts: Power · Properties of powers
Skills: Calculate
Exercise type: Evaluating expressions