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

Exponents … used to show repeated multiplication 2 x 2 x 2 = 23 “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…

Examples - evaluate 1) 73 2) -72 3) (-7)2 4) 41 5) 32(4)3 6) 2500 7) (-1)45 8) (-1)208

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.

Ex: evaluate 1) 6 – 6 + 8 2) -32 – 5(7 – 10)2 3) [4 + {(6 – 3)2 ÷ 3} 2] 2 4) 1 - 1 · 3 + 3 8 4 2 5

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