Download The Real Number System

Mathematics 9
Unit: Powers and Roots
Name:
Date:
Positive Exponents
Define: Base, Exponent, Power, Repeated Multiplication (Factored) Form,
Standard Form, Exponential Form, Variable, Coefficient
Remember: When an integer, other than 0, can be written as a product of
equal factors, we can write the integer as a power. Exponents are used as a
short way to write repeated multiplication.
Base
92
Power
Exponent
“Nine squared”
or
“Nine to the exponent two”
Standard Form Repeated Multiplication Form Exponential Form
81
9×9
92
125
5×5×5
53
Mathematics 9
Unit: Powers and Roots
Name:
Date:
Work with a partner
for this activity and
don’t forget to recycle
your paper when done!
Explore: When you repeatedly fold a piece of paper in half, the number of
layers increases with the number of folds. Fold a standard piece of paper,
and copy and complete the table.
Number of Folds
1
2
3
4
5
6
Number of Layers
(Repeated Multiplication, Standard, Exponential)
2 = 2 = 21
2 × 2 = 4 = 22
If you were to fold a piece of paper the following numbers of times, how
many layers would you have? Express each answer in exponential form.
a. 4
b. 8
c. 27
If 10 layers of paper are about 1 mm thick, how thick is a piece of paper
after 10 folds?
What is the maximum number of times you can fold a piece of paper?
Mathematics 9
Unit: Powers and Roots
Name:
Date:
Remember: If the base is given in brackets, do not get rid of the brackets!!
Class Example:
Write the following powers in repeated multiplication and standard form.
Exponential Form Repeated Multiplication Form Standard Form
74
Exponent only applies
to the number or
variable directly
underneath!
7×7×7×7
2401
2 2 2
  ×  × 
3 3 3
 8 
 
 27 
(-5)4
(-5) × (-5) × (-5) × (-5)
625
-54
-1 × 5 ×5 × 5 × 5
-625
2
 
3
3
Try On Your Own:
Write the following powers in repeated multiplication and standard form.
Exponential Form Repeated Multiplication Form Standard Form
-23
(-2)3
-(-5)6
34
Apply the rules for multiplying integers: The sign of a product with an
even number of negatives is positive. The sign of a product with an odd
number of negatives is negative. Example:
2
(-3) = (-3)(-3) = 9
(-3)3 = (-3)(-3)(-3) = (-27)
Even
Positive
Odd
Negative