Problem 6 · 2013 Math Kangaroo
Medium
Algebra & Patterns
number-systems
If you add \(4^{15}\) and \(8^{10}\), you obtain a number that is a power of two. Determine that number.
Show answer
Answer: E — \(2^{31}\)
Show hints
Hint 1 of 2
Rewrite both terms as powers of 2 before adding.
Still stuck? Show hint 2 →
Hint 2 of 2
Equal powers of 2 add to double one of them — that just bumps the exponent up by 1.
Show solution
Approach: express both terms with base 2
- 4¹⁵ = (2²)¹⁵ = 2³⁰ and 8¹⁰ = (2³)¹⁰ = 2³⁰.
- So the sum is 2³⁰ + 2³⁰ = 2 · 2³⁰ = 2³¹.
- The number is 2³¹.
Mark:
· log in to save