Rules of Exponents; Growth & Decay Problems

Rules of Exponents:

1. b ^xb ^y = b ^{x + y}
2. b ^x = b ^{x - y}
b ^y
3. (ab) ^x = a ^xb ^x
4. (a/b) ^x = a ^x
               b ^x
5. b ^x = b ^y if and only if x = y
6. a ^x = b ^x if and only if a = b
7. (b ^x) ^y = b ^xy
8. b⁰ = 1
9. b ^-x =  1
          b^x
10. b ^p/q = ^q\/(b ^p)

Some large numbers:

• Avagadro's Number:  6.02 x 10 ²³
• Googol:  10 ¹⁰⁰
• Googolplex ( googol of googols):  10 ²⁰⁰ (sometimes used to count stars in the universe)