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.
Practice
Solve:
1) X
X
3) X
X
2)
4)
X
X =
If X = 5
X
X
If X =3
=
Practice
• Solve:
• n=3
If x = 64
n=2
729
solve
x
Practice
• Write 12 as multiplication.
• Write u as a fraction using only positive
exponents.
• What is the value of 125
• Evaluate -4 and (-4)
?
Distributive Property
The Distributive Property of multiplication
is the property that states that multiplying
a sum by a number is the same as
multiplying each addend by the number
and then adding the products. The
Distributive Property says that if a, b and c
are real numbers,
then a(b + c) = (a x b) + (a x c)
Examples of Distributive property
36 + 8 = 44
Step 1
Step 2
Answer
4 (9 + 2) =
(4 x 9) + (4 x 2) =
36
+
8 = 44
Practice
1) 5 (x + 3)
2) x ( y + 9)
Are these equal?
3) 25 + 10 =
4) 5 + 3 =
7 (5
20 (3
+ 0) =
+ 1) =
Scientific Notation
Definition: A method of expressing numbers in
terms of a decimal number between 1 and 10
multiplied by a power of 10.
Example: The Scientific Notation for 10,492 is
1.0492 X 10 .
Show You Tube Video
Practice
Convert to Scientific notation
1) 7535
3) .00045
2) .0027
4) 8,456