ExponentsAn 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
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 (if X = 0) X
X = 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)
Solutions1) 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.
DifferencesMath is a language
• (4x) means (4 ) (X )
• 4x means 4 (X)(X)(X)
Dividing Exponents
Step 1: X X =
Step 2: X = 1 X
Step 3: (X ) (X ) = X
Dividing Exponents
Step 1: X X =
Step 2: (XX) (XXXXXX) (XXXXXX)
STEP 3: (XX) (XXXXXX) (XXXXXX)
Step 3: (XX) = X
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 2) X X = If X = 5
3) X X 4) X X = If X =3
Practice
• Solve: • n = 3 729
If x = 64 solve x n = 2
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 PropertyThe 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 4 (9 + 2) = Step 2 (4 x 9) + (4 x 2) = Answer 36 + 8 = 44
Practice
1) 5 (x + 3)
2) x ( y + 9)
Are these equal?
3) 25 + 10 = 7 (5 + 0) =
4) 5 + 3 = 20 (3 + 1) =
Scientific NotationDefinition: 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 2) .0027
3) .00045 4) 8,456
