1. Exponents and Order of Operations

2. 
 Exponent (power) – a number that indicates how
many times its base is used as a factor. In bx, x is the
exponent (power).
 Consider the prime factored form of 81
81=3∙3∙3∙3 (The factor 3 appears four times)
In algebra, repeated factors are written with an exponent,
so the product 3∙3∙3∙3 is written as 34 and read as “3 to the
fourth power.”
The number 4 is the exponent, or power, and 3 is the
base in the exponent expression 34.
Exponents

3. Example 1: Evaluate Exponential Expressions
a) 52 = 5∙5 = 25 (5 is used as a factor 2 times)
b) 63 = 6∙6∙6 = 216 (6 is used as a factor 3 times)
c) (0.3)2=0.3(0.3)=0.09
Raising Products to a Power
(6 × 7)3
= 63
× 73
= 74,088
Raising Quotients to a Power
(
2
3
)3=
23
33
2
3
∙
2
3
∙
2
3
=
8
27
 Any number to the power of 0 equals to 1.
Ex: 10=1 or 100=1
 Any number to the power of 1 equals to the number.
Ex: 41=4 or 121=12

4. 
Exponents Rules
Law Example
x1 = x 61 = 6
x0 = 1 70 = 1
x-1 = 1/x 4-1 = 1/4
xmxn = xm+n x2x3 = x2+3 = x5
xm/xn = xm-n x6/x2 = x6-2 = x4
(xm)n = xmn (x2)3 = x2×3 = x6
(xy)n = xnyn (xy)3 = x3y3
(x/y)n = xn/yn (x/y)2 = x2 / y2
x-n = 1/xn x-3 = 1/x3
Exponential Form Standard Form
52 5∙5
(0.3)2 (0.3)(0.3)
https://www.youtube.com/watch?v=A1wKTiBTsfk

5. 
Exponential Graph
This link below helps you to practice exponential graph:
Exponential Graph

6. 
1) 53 2) (
2
3
)4
To answer number 1 and 2 by the following questions.
 What is the base number?
 What is the exponent number?
 Convert these numbers into standard form.
 Calculate their values and estimate to the nearest tenth.
Exponents Problems

7. 
Exponents
1) 53
 What is the base number? The base number is 5.
 What is the exponent number? The exponential number is
3.
 Convert those numbers into standard form?
 Calculate their values. 125
2) (
2
3
)4
 What is the base number? The base number is
2
3
.
 What is the exponent number? The exponential number is
4.
 Convert those numbers into standard form?
 Calculate their values.
16
81
or 0.20

8. 
Order of Operations
If grouping symbols are present, simplify within them, innermost first (and above
and below fraction bars separately), in the following order.
Step 1 Apply all exponents
Step 2 Do any multiplications or divisions in the order in which they
occur, working from left to right.
Step 3 Do any additions or subtractions in the order in which they occur,
working from left to right.
If no grouping symbols are present, start with step 1.
Order of Operation and
Grouping
"Operations" means things like add, subtract, multiply, divide, squaring, etc. If it
isn't a number it is probably an operation.

9. Example 2: Using the Rules for Order of Operations
Find the value of each expression
a) 4 + 5 ∙ 6
= 4 + 30 Multiply.
= 34 Add.
b) 9(6+11)
= 9(17) Work inside parentheses.
= 153 Multiply.
c) 6 ∙ 8 + 5 ∙ 2
= 48 + 10 Multiply, working from left to right.
= 58 Add
d) 9 − 23 + 5
= 9 – 2 ∙ 2 ∙ 2 + 5 Add the exponent.
= 9 – 8 + 5 Multiply.
= 1 + 5 Subtract.
= 6 Add.

10. Example 3: Using Brackets and Fraction Bars as Grouping
Symbols
Simplify each expression.
a) 2[8 + 3(6 + 5)]
= 2[8 + 3(11)] Add inside parentheses.
= 2[8 + 33] Multiply inside brackets
= 2[41] Add inside brackets.
= 82 Multiply.
b)
4 5+3 +3
2 3 −1
Simplify the numerator and denominator separately.
=
4 8 +3
2 3 −1
Work inside parentheses.
=
32+3
6−1
Multiply.
=
35
5
or 7 Add and Subtract. Then divide.
Note: "Please Excuse My Dear Aunt Sally".
“Pudgy Elves May Demand A Snack”.
“Popcorn Every Monday Donuts Always Sunday”.

11. 
Order of Operation &
Grouping
 Evaluate each expressions and estimate the value to
the nearest tenth.
1) 13 + 5 ∙ 9 2)
1
4
∙
2
3
+
2
5
∙
11
3
3) 5 3 + 4 22
4)
4 6+2 +8(8−3)
6 4−2 −22 5) 2 + 3[5 + 4(2)]

12. 
Order of Operation &
Grouping
 Evaluate each expression and estimate the value to
the nearest tenth.
1) 13 + 5 ∙ 9 = 58 2)
1
4
∙
2
3
+
2
5
∙
11
3
=
16
81
or 0.20
3)5 3 + 4 22 =95 4)
4 6+2 +8(8−3)
6 4−2 −22 =9
5) 2 + 3[5 + 4(2)]=41