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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. 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.

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exponents

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

3

substituting variables for numbers
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)

3

3

variable
Variable
  • A variable is a symbol for a number we don’t know yet like X or Y.
integers
Integers
  • Integers include zero, positive and negative numbers. They do not include fractions.
laws of exponents
Laws of Exponents

N

X = (X)(X)…..(X) (N factors of X)

X = 1 (if X = 0)

X

X = X

-n

n

1/N

N

practice
Practice

3

  • Write 11 as multiplication.
  • Write u as a fraction using only positive exponents.
  • What is the value of 100 ?
  • Evaluate -5 and (-5)

-7

1/2

-2

-2

solutions
Solutions
  • 11 X 11 X 11 = 1331
  • 1

u

  • 10
  • 1

25

7

multiplying exponents
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.

5

6

11

differences math is a language
DifferencesMath is a language

3

3

3

  • (4x) means (4 ) (X )
  • 4x means 4 (X)(X)(X)

3

dividing exponents
Dividing Exponents

8

6

Step 1: X X =

Step 2: X =

1

X

Step 3: (X ) (X ) = X

8

6

2

8

-6

dividing exponents1
Dividing Exponents

8

6

Step 1: X X =

Step 2: (XX) (XXXXXX) (XXXXXX)

STEP 3: (XX) (XXXXXX)

(XXXXXX)

Step 3: (XX) = X

2

slide12
x

0

  • 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.

3

-3

3

3

practice1
Practice

Solve:

  • X X 2) X X =

If X = 5

3) X X 4) X X =

If X =3

3

2

2

0

-2

-2

4

7

practice2
Practice
  • Solve:
  • n = 3 729

If x = 64 solve x

n = 2

3

n

practice3
Practice

3

  • Write 12 as multiplication.
  • Write u as a fraction using only positive exponents.
  • What is the value of 125 ?
  • Evaluate -4 and (-4)

-5

1/3

-2

-2

distributive property

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
Examples of Distributive property

36 + 8 = 44 Step 1 4 (9 + 2) =

Step 2 (4 x 9) + (4 x 2) =

Answer 36 + 8 = 44

practice4
Practice
  • 5 (x + 3)

2) x ( y + 9)

Are these equal?

3) 25 + 10 = 7 (5 + 0) =

4) 5 + 3 = 20 (3 + 1) =

2

scientific notation

Scientific Notation

4

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

practice5
Practice

Convert to Scientific notation

  • 7535 2) .0027

3) .00045 4) 8,456

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