Naming the parts
When you write 3^4, you are saying “multiply 3 by itself 4 times.” The number being multiplied is the base; the small raised number that counts the copies is the exponent; and the whole expression — together with its value — is called a power. So 3^4 = 3 · 3 · 3 · 3 = 81. The base tells you what is multiplied; the exponent tells you how many factors there are.
3^4 means 3 · 3 · 3 · 3
= 9 · 3 · 3
= 27 · 3
= 81
base = 3 exponent = 4 power = 81The exponent is not a multiplier
The single most common beginner slip is treating the exponent like a factor: writing 3^4 = 3 · 4 = 12. It is not. The exponent counts factors of the base — it never multiplies the base directly. A quick reality check: 2^3 should be 8, and indeed 2 · 2 · 2 = 8, while 2 · 3 would only give 6. When in doubt, write out the factors and evaluate them honestly.
Powers come early in the order of operations: you evaluate exponents before multiplication, division, addition, or subtraction. So in 2 · 3^2 you do the 3^2 = 9 first, then 2 · 9 = 18 — not (2 · 3)^2 = 36.