Powers and exponents describe how to multiply a number by itself a specified number of times. The exponent tells you how many times the base number is used as a factor. Following the order of operations (PEMDAS/BODMAS), you complete all exponent/power calculations before multiplication or division, and perform operations from left to right within each type. Some examples show calculating exponential expressions like 65 = 7,776 and ordering expressions using comparisons like 10 3 < 5 5.

1. Powers and
Exponents

2. 3
base
exponent
This can be read as:
2 raised to the power of 3 or
2 raise to the third power
This means:
2 × 2 × 2 = 8

3. • Exponent – tells how many times a
number is a multiplied by
itself.
• Exponential notation
72
= 49
• Expanded notation
7 × 7 = 49

4. Example:
65
= 6 × 6 × 6 × 6 × 6
= 7,776
43
= 4 × 4 × 4
= 64
33
= 3 × 3 × 3
= 27

5. Activity!
Give the value of each expression on the line.
8
3
= __________ 10
5
= __________
2
4
= __________ 5
7
= __________
9
6
= __________
Write <, >, or = in each box.
10
3
5
5
4
4
2
8
9
3
3
9

6. Order of
Operations

7. • The standard order of operations for
computations involving more than one
mathematical operation is GEMDAS.
G – grouping (), {}, []
E – exponent a2
M – multiplication ×
D – division ÷
A – addition +
S – subtraction ̶

8. Steps in the
Order of Operation
100 ̶ (8+2) × 32
÷ 2 =
• Step 1: Compute all the operations enclosed in
grouping symbols, that is, parentheses (), brackets
[], and braces {}.
• Step 2: Compute all powers or exponents.
100 ̶ (8+2) × 3
2
÷ 2 = 100 ̶ 10 × 3
2
÷ 2
100 ̶ (8+2) × 3
2
÷ 2 = 100 ̶ 10 × 3
2
÷ 2
= 100 ̶ 10 × 9 ÷ 2

9. • Step 3: Multiply and divide in order
from left to right.
• Step 4: Add and subtract in order from
left to right.
100 ̶ (8+2) × 3
2
÷ 2 = 100 ̶ 10 × 3
2
÷ 2
= 100 ̶ 10 × 9 ÷ 2
= 100 ̶ 90 ÷ 2
= 100 ̶ 45
100 ̶ (8+2) × 3
2
÷ 2 = 100 ̶ 10 × 3
2
÷ 2
= 100 ̶ 10 × 9 ÷ 2
= 100 ̶ 90 ÷ 2
= 100 ̶ 45
= 55