2.6 Order of Operations (p.48-51)

I. Follow this order for evaluating expressions with more than one operation.
1. First, perform operations in parentheses.
2. Clear exponents by replacing with the real value.
3. Multiply and divide, working from left to right.
4. Add and subtract, from left to right.

Ways to Remember

• Parentheses - Exponents - Multiply and Divide - Add and Subtract
  P-E-(MD)-(AS) or "PEMDAS "
• Please (parentheses) Excuse (exponents)My Dear (multiply and divide) Aunt Sally (add and subtract)
  
  Example:
  285+93÷(3-2) x 3 x4²
  285+93÷ 1 x 3 x4² parentheses
  285+93÷1x 3 x16 exponents
  285+93÷1 x3x16 multiply and divide from left to right
  93 x3= 279
  279 x 16 = 4464
  285 + 4464 = 4749 add and subtract
  
  285+93÷(3-2) x 3 x4² =4749
  

For a description of how order of operations works try this link that includes an explanation and practice problems from mathgoodies.com

Here is a game from Harcourt to see how well you know your operations.
Play Rags to Riches to test what you know.

Take this Quiz from math6.org

2.5 Exponents (p.46-47)

I. Exponent: a symbol of repeated multiplication
A. An exponent shows how many times a number is multiplied by itself.
B. Exponent can also be called a "power"

II. Base: the number being multiplied (used as a factor) when working with exponents.
Examples:
The exponent "2" is telling us to multiply the base "4" "2" times. 4x4 =16
III. Rules:
A. Using the power of 1, makes the value equal to the base (original) number
B. Using "0" power of any number, expcept zero, is defined to be 1

IV. Reading exponents: aⁿ or a^n

• a raised to the n-th power,
• a raised to the power [of] n or possibly a raised to the exponent [of] n,
• a to the n-th power or a to the power [of] n,
• a to the n.

A. Some exponents have their own pronunciation: for example, a^2 is usually read as a squared and a^3 as a cubed.

Here is a brief description of exponents from About.com.
Check what you know on this short quiz and get immediate feedback from regentsprep.org.