Prerequisites: Reviewing Numbers

Exponents

Take a few minutes to review the rules for exponents. For a more thorough review, see Appendix A Mathematical Review, A-2 in your textbook.

Key concept General Exponent Rules

Rule
Example
Power of Zero
a raised to the zero power equals one
Negative Exponents
a raised to the negative n equals one divided by a to the n power
Negative Numbers with Exponents
the quantity negative a to the even power equals a to the even power
the quantity negative a to the odd power equals negative a to the odd power
Multiplying Numbers of the Same Base
a to the n power times a to the m power equals a to the power of n plus m
Multiplying Different Numbers with the Same Exponent
a to the n power times b to the n power equals the quantity a times b end quantity raised to the n power
Raising a Number with an Exponent to a Power
the quantity a to the n power raised to the m power equals a raised to the power of n times m

 

Examples

  1. x raised to the power of five times x raised to the power of negative three equals x raised to the power of five minus three equals x raised to the power of two
  2. a raised to the power of three times a raised to the power of negative three equals a to the power of three minus three equals a to the zero power equals one or a raised to the power of three times a raised to the power of negative three equals a raised to the power of three divided by a raised to the power of three equals one
  3. five to the power of three times six to the power of three equals the quantity five times six all raised to the power of three equals thirty to the power of three equals twenty seven thousand
  4. the quantity n raised to the one half power end quantity raised to the second power equals n raised to the power of one half times two equals n