1. Powers & Roots
When we say an integer or real number is “raised to a power”, we are talking about exponents.

2. Powers & Roots
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.

3. Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.
𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡

4. Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.
𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
Here are some examples : , (−4) 3 , 2 5

5. Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.
𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
Here are some examples : , (−4) 3 , 2 5
To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent.

6. Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.
𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
Here are some examples : , (−4) 3 , 2 5
To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent.
For example : =2×2×2 ( take your base 2 and multiply it three times )

7. Powers & Roots 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
When we say an integer or real number is “raised to a power”, we are talking about exponents.
Exponents appear as a small number superscripted above a base.
𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡
Here are some examples : , (−4) 3 , 2 5
To evaluate these numbers, we take the base, and then multiply that base the number of times given by the exponent.
For example : =2×2×2 ( take your base 2 and multiply it three times )
(−4) 4 =(−4)×(−4)×(−4)×(−4)

8. Powers & Roots
An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button.

9. Powers & Roots
An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button.
EXAMPLES : Using a calculator evaluate
2 3 Press 2 , ^ , 3 , = answer is 8

10. Powers & Roots
An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button.
EXAMPLES : Using a calculator evaluate
2 3 Press 2 , ^ , 3 , = answer is 8
3 5 Press 3 , ^ , 5 , = answer is 243

11. Powers & Roots
An easier way to evaluate these is by use of a calculator. The ^ button on the calculator is located above the 𝑥 2 button.
EXAMPLES : Using a calculator evaluate
2 3 Press 2 , ^ , 3 , = answer is 8
3 5 Press 3 , ^ , 5 , = answer is 243
(−4) 2 Press ( , - , 4 , ) , ^ , 2 , = answer is 16

12. Powers & Roots
We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number.

13. Powers & Roots
We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 )

14. Powers & Roots EXAMPLES : 4 , 25 , 3 8
We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 )
EXAMPLES : , ,

15. Powers & Roots EXAMPLES : 4 , 25 , 3 8
We will also be using roots in our work. A root of a number is a quantity that is taken two or more times as an equal factor of the number. The symbol for a root 𝑖𝑛𝑑𝑒𝑥 𝑏𝑎𝑠𝑒 has some base under what is called a “radical”. The root taken is understood to be a 2, unless otherwise shown by the index. If there is no index shown, we take the square root ( index = 2 )
EXAMPLES : , ,
** warning – you CAN NOT take an even indexed root of a negative value.

16. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.

17. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.

18. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =

19. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10

20. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =

21. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )

22. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button 𝑥

23. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button
It will calculate any root greater than 2. 𝑥

24. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button
It will calculate any root greater than 2.
To evaluate you enter , 2nd , ^ , 8 , = 𝑥

25. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button
It will calculate any root greater than 2.
To evaluate you enter , 2nd , ^ , 8 , = ANSWER is 2 𝑥

26. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button
It will calculate any root greater than 2.
To evaluate you enter , 2nd , ^ , 8 , = ANSWER is 2
To evaluate you enter 4 , 2nd , ^ , 10 , = 𝑥

27. Powers & Roots
I zoomed in on the calculator to show you what buttons we will be using to evaluate square roots when instructed.
Above the 𝑥 2 button in blue you will find the square root button.
To evaluate you enter 2nd ( blue button top left ) , 𝑥 2 , 100 , =
ANSWER = 10
To evaluate you enter 2nd , 𝑥 2 , 12 , =
ANSWER = ( rounded )
Above the ^ button is the nth root button
It will calculate any root greater than 2.
To evaluate you enter , 2nd , ^ , 8 , = ANSWER is 2
To evaluate you enter 4 , 2nd , ^ , 10 , = ANSWER is ( rouned ) 𝑥