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## PowerPoint Slideshow about ' Exponents' - zytka

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### Exponents

### Distributive Property

### Scientific Notation

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.
- For example:
3 = 3 X 3 X 3 = 27 SO: X = (X)(X)(X)

3

3

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.

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

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

Dividing Exponents

8

6

Step 1: X X =

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

STEP 3: (XX) (XXXXXX)

(XXXXXX)

Step 3: (XX) = X

2

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

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

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 4 (9 + 2) =

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

Answer 36 + 8 = 44

Practice

- 5 (x + 3)
2) x ( y + 9)

Are these equal?

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

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

2

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 .

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