What is a power tower?

A power tower is an exponential expression where the exponent itself is an exponential expression, and so on. For example, a b c means a raised to the power of (b raised to the power of c).

How do you compare them without a calculator?

The general rule is that the taller the tower, the larger the number. For towers of the same height, the top-most difference usually decides the winner because exponents grow much faster than their bases. You can also use the rule that a b is larger than c d if b·log(a) is larger than d·log(c).

Is 5 5 11 larger than 2 2 2 4 2 ?

No, 2 2 2 4 2 is significantly larger. Despite the smaller base, the height and the values higher up in the stack of the second tower make it grow much faster than the first.

Yes. Higher difficulty introduces taller towers and values that are closer together, requiring more careful logarithmic reasoning.

Can I print it as a worksheet?

Yes. Power Towers supports the printable worksheet generator at /worksheets · each problem prints two towers with a lettered choice for the larger one and an answer key.

Power Towers · Українська

Which power tower is larger? Compare exponential stacks using logarithmic logic and number sense

Which power tower is larger? Compare exponential stacks using number sense and logarithmic logic. JavaScript required.

Enable JavaScript to play.