Download Exponents - Sage Middle School

Exponents
An exponent is the number of times the base is
multiplied by itself.
Example
27 can also be written as 3
This means 3 X 3 X 3
Substituting variables for numbers
• We can also use variables such as X and Y
when using exponents. We can define X and Y
as integers.
• For example:
3
= 3 X 3 X 3 = 27 SO: X = (X)(X)(X)
Variable
• A variable is a symbol for a number we don’t
know yet like X or Y.
Integers
• Integers include zero, positive and negative
numbers. They do not include fractions.
Laws of Exponents
X = (X)(X)…..(X) (N factors of X)
X
= 1
X
X
=
(if X = 0)
X
Practice
• Write 11 as multiplication.
• Write u as a fraction using only positive
exponents.
• What is the value of 100
• Evaluate -5 and (-5)
?
Solutions
1) 11 X 11 X 11 = 1331
2) 1
u
3) 10
4) 1
25
Multiplying Exponents
• Same base
• (X ) (X)
= X
• Be careful I can add the exponents, because X
is the base both time. If I had X and Y I could
only combine in the exponents were the
same.
Differences
Math is a language
• (4x)
• 4x
means (4 ) (X )
means 4 (X)(X)(X)
Dividing Exponents
Step 1: X
Step 2:
Step 3:
X =
X
1
X
=
(X ) (X ) = X
Dividing Exponents
Step 1: X
Step 2:
X =
(XX) (XXXXXX)
STEP 3: (XX) (XXXXXX)
(XXXXXX)
Step 3:
(XX) = X
(XXXXXX)
x
• Anything divided by itself is 1. X to the zero
power is 1.
• Example
X /X
= (X ) (X )
=1
• This works in all cases except for if X is equal
to zero.