Exponents

Things one must know:

• An even exponents hides the sign of the base
• Numbers between 0 and 1 decrease when raised to a higher exponents
• Exponents rules! (MGMAT NP p68)
• Exponential expressions can only be simplified if they are linked by multiplication or division and have either a base or an exponent in common
• Terms added or subtracted can be factored whenever the base is the same or whenever the exponent is the same and bases contain something in common
• An exponent of 0 always yields 1
  
• A base of 0 always yields 0
• A base of 1 always yields 1, -1 yields 1 if the exponent is even and -1 if the exponent is odd
• Always considering factoring or distributing a given expression if it's possible. 
• 4 step simplifying process: 1) simplify or factor an additive or subtractive terms; 2) break every non-prime base down into prime factors; 3) distribute the exponents to every prime factor; 4) combine the exponents for each prime factor and simply.
• Advanced distributed/factored forms (MGMAT NP p164)