1. Exponents, Parentheses, and the Order of Operations
Section 1.9
Exponents, Parentheses, and the Order of Operations

2. Exponents … used to show repeated multiplication
2 x 2 x 2 = “2 to the third power”
Special case: Any number to the zero power is one: n0 = 1
When the base is negative, consider if the negative is INCLUDED in parentheses or not…

3. Examples - evaluate
1) 73 2) -72 3) (-7)2 4) 41 5) 32(4)3 6) ) (-1)45 8) (-1)208

4. Order of Operations (PEMDAS)
P – Do any operations in parentheses first.
For NESTED parentheses - work from the innermost set out.
E – Evaluate any exponents next.
MD – Multiply or Divide in order from left to right.
AS – Add or Subtract in order from left to right.

5. Ex: evaluate
1) 6 – ) -32 – 5(7 – 10)2 3) [4 + {(6 – 3)2 ÷ 3} 2] 2 4) ·

6. Evaluate
5) [5 – (3 – 7) – 2]2 2[(16 ÷ 22) – (8 ·4)] 6) [-3 + (48 ÷ 42) 7) (-3)3 + 8 ÷ 2(-7) 8) 2x3 + x2 – 6 (use x = -2)