1. Warm-Up Write an algebraic expression for the following phrases.
5 less than the product of 3 and a number t.
Twice the sum of a number b and 8.
Try to translate the algebraic phrase into a verbal phrase.
3. 4 – (d / 6)
4. (x + 7) / 2

2. 1.2 – Order of Operations and Evaluating Expressions
Goals:
to simplify expressions involving exponents
to use the order of operations to evaluate expressions

3. Simplifying Powers: power nth power base exponent
An expression like xn is called a ________________ and is read “x to the _____ ______________.” x is called the ______________ (the number being multiplied) and the n is called the _______________ (it tells how many times the base is used as a factor.)
power
nth
power
base
exponent

4. 8 8 8 ● 8 64 8● 8● 8 512 8 ●8 ●8 ●8 4096 8 ●n ●n ●n ●n ●n 1st 2nd
squared
3rd
8● 8● 8
512
cubed
4th
8 ●8 ●8 ●8
4096
times
8 ●n ●n ●n ●n ●n
Depends on the value of “n”
5th

5. Evaluating Powers
2●2 ●2 ●2 ●2 ●2 64 64
4●4 ●4
32,768

6. Practice:

7. Simplifying a Numerical Expression
grouping symbols
innermost
parentheses ( )
brackets [ ]
braces { }
radical sign
fraction bar
exponents
multiplication
division
left
right
addition
subtraction
left
right

8. 48 ÷ 8 ● 3 + 5
6● 3 + 5
18 + 5 23
– 3
26 – 3 23
6 + 4 – 6
10 – 6 4

9. Evaluate the expressions for x = 3 and y = 5.
Evaluate the expressions for a = 2 and b = 6
x + y2 – xy
(y – x) + 4(xy)
3. (a + b)2
a2 + b2