Math 12 – Laws of Exponentiation

 

Exponentiation is an operation (just like addition and multiplication are operations) which means “raising to a power.” When you simplify a mathematical expression that contains exponents, you must complete the operations according to the Order of Operations (BEDMAS).  Exponents are completed before any other operation except those within brackets. 

 

Mathematical Agreement: An exponent only affects one symbol (the one right next to it).  If you want the base of an exponent to consist of more than one symbol, then it must be placed in brackets.  For example,  -1² = -1, but (-1)² = +1.  In the first case, the one is squared and then multiplied by a negative.  In the second case, the -1 is squared (i.e. -1 x -1 = +1).

 

 

Exponent Laws

• Multiplication Law      
• Division Law                  
• Power of a Power
• Power of a Product
• Power of a Quotient
• Negative Exponents         
• Zero Exponents , provided x ≠ 0
• (This is the new one!) Rational Exponent Law

 

 

Examples: Simplify the following: (...leave no negative or rational exponents)

 

1.                             Multiplication Law

2.                             Multiplication Law

3.                Division Law and Negative Exponents

4.                                      Division Law

5.                      Division Law and Negative Exponents