1. 6.1.2 Powers and Exponents

2. Vocabulary Review Operation Words Algebra Addition The sum of a + b
Subtraction
The difference of
a – b
Multiplication
The product of
a x b a · b (a)(b) ab
Division
The quotient of
a ÷ b a/b b a

3. Vocabulary Base – the repeated factor Power – a factor and exponent
In the examples to the right, 5 is the base
Product – multiplication answer
36 is a product of 6 x 6
6 x 6 is also a product, it’s just not solved yet
Power – a factor and exponent
Example: 5³
“5 to the third power”
“5 to the power of three”
“5 cubed”
Exponent – the number of times to repeat a factor
In the examples above, 3 is the exponent

4. Why squared? Why cubed?
A factor to the power of 2 is called “squared”
A factor to the power of 3 is called “cubed”
A factor to the power of 4 is called “fourth power”…5 is “fifth power” and so on
Here’s why…
To find the area of a SQUARE, you multiply TWO sides
To find the area of a CUBE, you multiply THREE sides 3 2 2 1 1

5. Write the product as a power
5 · 5 · 5 · 5 · 5 · 5
Because 5 is used as a factor six times, the exponent is 6
So, 5 · 5 · 5 · 5 · 5 · 5 = 5⁶
5 is the base; 6 is the exponent
13 · 13 · 13 · 13
Because 13 is used as a factor four times, the exponent is 4
So, 13 · 13 · 13 · 13 = 13⁴
13 is the base; 4 is the exponent

6. Your turn
Write each of the products below as an exponent: 6 · 6 · 6 · 6 · 6 = 2 · 2 · 2 · 2 = 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 = 9 · 9 = 31 · 31 · 31 =

7. Finding the values of Powers
Write the power as repeated multiplication 7² = 7 · 7 then simplify = 49 5³ = 5 · 5 · 5 = 125

8. Perfect squares The square of a whole number is a perfect square
Here are a few perfect squares:
36 (6 · 6 or 6²)
25 (5 · 5 or 5²)
81 (9 · 9 or 9²)
What is 16 a perfect square of?
What is 100 a perfect square of?
What is 121 a perfect square of?

9. Your Turn Find the value of the power 6³ = 3⁴ = 18² =
Determine if the number is a perfect square
25 yes or no
2 yes or no
99 yes or no
49 yes or no

10. Homework
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