🧱 See It
Writing 2 × 2 × 2 × 2 every time is tedious. An exponent is shorthand for exactly that — "multiply this number by itself, this many times":
2
2
2
2
4 twos multiplied together, written as 2⁴.
✏️ Draw It
| Written out | Exponent form | Value |
|---|---|---|
| 2 × 2 × 2 × 2 | 2⁴ | 16 |
| x × x × x | x³ | — |
The base (bottom number) is what's being multiplied. The exponent (small raised number) says how many times.
🔢 Write It
2⁴ = 2 × 2 × 2 × 2 = 16
Watch what happens dividing by 2 each step down the exponent:
| 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
|---|---|---|---|---|
| 16 | 8 | 4 | 2 | 1 |
Any number (except 0) raised to the power of 0 equals 1 — not because it's an arbitrary rule, but because the pattern of dividing by the base keeps working right down to the last step.
💡 Worked Examples
Example 1: 3⁴
- Write it out fully:
3 × 3 × 3 × 3 - Multiply step by step:
3 × 3 = 9, then9 × 3 = 27, then27 × 3 = 81 - Answer:
81
Example 2: 7⁰
- Any nonzero base to the power of 0 is 1 — no multiplying needed.
- Answer:
1
🧠 Quick Reference
The exponent tells you how many times to multiply the base by itself — it is NOT the same as multiplying by the exponent.
2⁴ means 2×2×2×2 = 16, never 2×4 = 8. Anything (except 0) to the power of 0 is 1.