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 .

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Practice

Convert to Scientific notation

1)7535 2) .0027

3) .00045 4) 8,456