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MATH IS FUN!!! M8N1 Students will understand different representations of numbers including square roots, exponents, and scientific notation. Element: i. Simplify expressions containing integer exponents. We have come to ZAPP the Powers from the Earthlings. SPONGE.

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slide1

MATH IS FUN!!!M8N1 Students willunderstand different representations of numbers including square roots, exponents, and scientific notation.Element: i. Simplify expressions containing integer exponents.

We have come to ZAPP the Powers from the Earthlings

sponge
SPONGE

WHAT IS ANOTHER WAY TO WRITE

6 X 6 ?

REVIEW: WRITE A NUMBER FOR EACH

Whole

Natural or Counting

Real Number

Rational

Irrational

Integer

slide3
M8N1

Let’s start by reviewing exponent laws!

multiplying powers
Multiplying powers …
  • If you are multiplyingpowers with the same base …

34 x 36

(here both numbers have a base of 3)

Then … you keep the base the same and ADD the exponents

34 x 36 = 3 (4 + 6)

= 310

try these do them on a sheet with your name and the date they will be collected next class
Try These…(Do them on a sheet with your name and the date – they will be collected next class!)

Simplify.

  • (32)(34)
dividing powers
Dividing powers …
  • If you are dividingpowers with the same base …

75

73

Then … you keep the base the same and you SUBTRACT the exponents

75٪ 73 = 7 (5 - 3)

= 72

do these on your page
Do these on your page …

Simplify.

1. 25

22

2. k4

k

exponents of exponents
Exponents of exponents …
  • If you have to simplify a power of a power with the same base …

(25)3

Then … keep the base the same and MULTIPLY the exponents

(25)3 = 25x3

= 215

do these on your page1
Do these on your page …

Express as a single power.

  • (103)2
  • (2813)0
  • (6-1)-1
zero as an exponent
Zero As An Exponent

Except for 0, any base raised to the 0 power simplifies to be the number 1.

Note that the exponent doesn’t become 1, but the whole expression simplifies to be the number 1.

3^0 = 1 

but what if there are numbers and variables
But what if there are numbers and variables???

(-x2)100

The exponent must still be applied to EVERYTHING inside the bracket!

(-x2)100 is the same as (-1x2)100

In this case, the 100 applies to the -1 AND the x2

(-1x2)100 = (-1)100(x2)100

= 1x2x100

= 1x200

ok now for something a little bit new
Ok, now for something a little bit new!!!

You know how to simplify expressions with exponents, but sometimes you are asked to evaluate them after they are simplified.

BUT … what do you do with a negative exponent?!?

3 2 3 1
(3-2)(3-1)

We know that when we multiply powers with the same base, we ADD the exponents …

(3-2)(3-1) = 3(-2 + -1)

= 3-3

How do we evaluate this??

slide14
3-3

Anytime you have a negative exponent, you can make it into a positive exponent by putting a 1 over number!

3-3 = 1

33

= 1

9

let s see another one of those
Let’s see another one of those …

If we have the following:

5-7 remember we SUBTRACT the

5-3 exponents

5-7 = 5(-7 - -3) = 5-4

5-3

Now, we simply put 5-4 under a 1  1_

54 (it becomes positive)

And we can evaluate it as we would any positive exponent …

1 = 1

54 625

work period cmp2 operating with exponents
WORK PERIODCMP2Operating With Exponents

From page in your textbook: Growing, Growing, Growing Page 62, 5.2

GROUPS: 3-4

Questions: A-D

Presentations: Students will present

closing journal writing
Closing/Journal Writing

How are the rules for multiplying and dividing powers of the same base alike? How are they different?

home work
HOME WORK

WORKSHEET: GOOD LUCK

EARTHLINGS