IMO Practice Test — Exponents & Powers
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
Find the value of 2^3 + 3^2 - 4^1 + 5^0.
10
12
14
16
Explanation: 8 + 9 - 4 + 1 = 14
Question 2 of 6
hard
If 2^n = 64, find 3^(n-2).
9
27
81
243
Explanation: 2^6=64, so n=6. Then 3^(6-2) = 3^4 = 81.
Question 3 of 6
hard
(-1)^99 + (-1)^100 + (-1)^101 = ?
-3
-1
1
3
Explanation: (-1)^99=-1, (-1)^100=+1, (-1)^101=-1. Total = -1+1+(-1) = -1.
Question 4 of 6
hard
Simplify: (2^8 x 3^5) / (2^6 x 3^3). Which of the following equals this?
2^2 x 3^2
4 x 9
36
All of the above
Explanation: 2^(8-6)=2^2=4, 3^(5-3)=3^2=9. Product=36. And 2^2 x 3^2=4x9=36. So all are correct.
Question 5 of 6
hard
If 5^x = 125 and 2^y = 32, find x + y.
5
7
8
10
Explanation: 5^3=125, so x=3. 2^5=32, so y=5. x+y=3+5=8.
Question 6 of 6
hard
Among 2^10, 4^5, 8^3, and 16^2, which two are the largest?
2^10 only
4^5 only
8^3 only
2^10 and 4^5 are equal and largest
Explanation: 2^10=1024, 4^5=(2^2)^5=2^10=1024, 8^3=(2^3)^3=2^9=512, 16^2=(2^4)^2=2^8=256. So 2^10 and 4^5 are both 1024 and largest.