Problem 7 · 1993 AJHSME
Medium
Number Theory
exponent-rules
33 + 33 + 33 =
Show answer
Answer: A — 3⁴.
Show hints
Hint 1 of 2
This is adding, not multiplying — and adding three identical things is just multiplying by 3. Rewrite the sum as a single product before touching exponents.
Still stuck? Show hint 2 →
Hint 2 of 2
The key principle: addition of equal powers turns into a count out front (3×3³), and the count 3 is itself 3¹. Then multiplying powers of the same base means adding the exponents.
Show solution
Approach: turn repeated addition into multiplication, then add exponents
- Three copies of 3³ added together is 3 × 3³. Don't multiply the powers — when you ADD equal terms, you count them.
- Now 3 × 3³ = 3¹ × 3³, and multiplying same-base powers adds exponents: 1 + 3 = 4. So the answer is 3⁴.
- Trap to dodge: the tempting wrong moves all show up as choices — 9³ (adding the bases), 3⁹ (multiplying the exponents). Neither is what 'add three of them' means. Slow down on whether you're adding or multiplying.
Mark:
· log in to save