CEMC Pascal

Algebra Difficulty 1.4 Junior Find the answer

If $a$ and $b$ are positive integers, the operation $abla$ is defined by $a abla b=a^{b} imes b^{a}$ . What is the value of $2 abla 3$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $a abla b=a^{b} imes b^{a}$ , then $2 abla 3=2^{3} imes 3^{2}=8 imes 9=72$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.