Repeated Multiplication
Exponents are simply a shorthand for repeated multiplication. Instead of writing 2 × 2 × 2 × 2 × 2, you write 25. This is surprisingly powerful in the real world.
Real-World Examples
- Computers: Everything digital is based on powers of 2. A "Kilobyte" isn't 1000 bytes—it's 210 (1,024 bytes).
- Bacteria Growth: Some bacteria double every 20 minutes. If you start with 1, after 10 cycles (3 hours), you have 210 = 1,024 bacteria!
- Richter Scale: Earthquakes use a logarithmic scale. A magnitude 6.0 quake is 10 times stronger than a 5.0 (101 difference).
Tricky Rules Explained
Why is x0 always 1?
Think of it this way: 23 = 8, 22 = 4, 21 = 2. Notice we divide by 2 each step? So 20 must be 2 ÷ 2 = 1.
What does a negative exponent mean?
A negative exponent doesn't make the number negative; it makes it
small. It tells you to divide 1 by the number.
Example: 2-2 is
the same as 1/(22) which equals 1/4 (0.25).