Download presentation

Presentation is loading. Please wait.

Published byDwayne Nash Modified over 5 years ago

1
EXPONENTS

2
EXPONENTIAL NOTATION X IS THE BASE 2 IS THE EXPONENT OR POWER

3
EXPONENTIAL NOTATION THE BASE IS SQUARED

4
EXPONENTIAL NOTATION EXPONENT IS THE NUMBER OF TIMES THE BASE IS MULTIPLIED BY ITSELF

5
EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

6
EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

7
Compare these two cases 6 IS THE BASE (THE NEG. SIGN IS NOT PART OF THE BASE, IT MUST REMAIN PART OF THE ANSWER) -6 IS THE BASE

8
EXPONENTIAL NOTATION WHAT IS THE BASE? WHAT WILL BE SQUARED?

9
EXPONENTIAL NOTATION WHAT IS THE BASE? -h is the base

10
EXPONENTIAL NOTATION WHAT IS THE BASE? What will be raised to the 5th power?

11
EXPONENTIAL NOTATION WHAT IS THE BASE? r will be raised to the 5th power

12
TRY THESE

14
EVALUATING EXPRESSIONS WITH EXPONENTS

15
Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3

16
Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2x 2 (x+y) = 2(6) 2 (6+3)

17
Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2.Use PEMDAS 2x 2 (x+y) = 2(6) 2 (6+3) = 2(6) 2 (9) = 2(36)9 = 729 = 648

18
MULTIPLYING SIMILAR BASES X X2X2 X

19
THE RULE IS TO ADD THE EXPONENTS

20
MULTIPLYING SIMILAR BASES

22
TRY THESE PROBLEMS

23
DIVIDING SIMILAR BASES

24
THE RULE IS TO SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR

25
DIVIDING SIMILAR BASES THE RULE IS TO SUBTRACT THE EXPONENTS

26
TRY THESE

28
NEGATIVE EXPONENTS You can change a negative exponent to positive by switching it’s base from numerator to denominator or vice versa.

29
NEGATIVE EXPONENTS MOVE THE BASE & EXPONENT FROM THE NUMERATOR TO THE DENOMINATOR OR VICE VERSA AND CHANGE THE SIGN OF THE EXPONENT

30
NEGATIVE EXPONENTS X 2 /X 2 IS WHAT PROPERTY?

31
MULTIPLY NUMERATORS & MULTIPLY DENOMINATORS NEGATIVE EXPONENTS

32
ANYTHING TO THE ZERO POWER IS EQUAL TO ? NEGATIVE EXPONENTS

33
Why is anything to the zero power equal to 1?

34
Check Out These Patterns

35
Or For Anything

36
THIS IS WHY SWITCHING A NEGATIVE EXPONENT CHANGES ITS SIGN

37
Let’s compare the Neg. Exponent Rule with the Dividing Fraction Rule To divide fractions you INVERT THE 2ND FRACTION AND CHANGE THE DIVISION SIGN TO MULTIPICATION For negative exponents you INVERT THE BASE WITH AND CHANGE THE SIGN OF THE EXPONENT

38
Try These

40
What if the negative exponent is in the denominator? The same rule of inverting the base with the exponent and making the exponent positive applies but let see why this is so.

41
What if the negative exponent is in the denominator? Use the Multiplicative Identity to Simplify

42
What if the negative exponent is in the denominator? Do you remember what x 0 is equal to?

43
What if the negative exponent is in the denominator? INVERT AND CHANGE EXPONENT SIGN

44
Try These

45
Try These ANSWERS

46
SUMMARY SO FAR DIVIDING EXPONENTS SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR MULTIPLYING EXPONENTS ADD THE EXPONENTS INVERTING A NEGATIVE EXPONENT CHANGES ITS SIGN

47
DON’T BE MARY TO THE Z POWER GET WITH IT!

48
POWER TO A POWER THIS IS A POWERFUL IDEA

49
POWER TO A POWER VS. MULT. SIMILAR BASES

50
POWER TO A POWER MULTIPLY THE EXPONENTS

51
POWER TO A POWER Express Answers as Positive Exponents

52
POWER TO A POWER

53
COMPARING MULTIPLY SIMILAR BASES & POWER TO A POWER

54
WHAT’S THE DIFFERENCE?

56
NOTHING REALLY (A MONOMIAL IS A PRODUCT) A monomial is a term with a number and one or more variables (letters) raised to some power. Examples are:

58
Let’s take a close look at DISTRIBUTING THE POWER

59
Simplify (4d 5 ) 2 Power of a Monomial

60
Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 1.Multiply the outside power to the inside powers. Power of a Monomial

61
Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 = 16 d 10 1.Multiply the outside power to the inside powers. 2.Simplify Power of a Monomial

62
Simplify (2x 3 y 4 ) 5 1.Multiply the outside power to the inside powers. 2.Simplify

63
Power of a Monomial Simplify (2x 3 y 4 ) 5 = 2 15 x 35 y 45 = 2 5 x 15 y 20 or 32 x 15 y 20 1.Multiply the outside power to the inside powers. 2.Simplify

64
Take a Power of a Quotient Simplify

65
Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers.

66
Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers. 2.Simplify

67
Mult/Divide Monomials with Exponents

68
1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents.

69
Mult/Divide Monomials with Exponents 1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents. 3.Simplify

70
5 Exponent Rules 1.When multiplying similar bases add exponents 2.When dividing similar bases subtract exponents 3.When inverting change exponents’ sign 4.When taking a power of a power multiply exponents 5.When taking a power of a product or quotient distribute the outside power to the inside powers

71
DIVIDING EXPONENTS SUBTRACT THE EXPONENTS MULTIPLYING EXPONENTS ADD THE EXPONENTS Anything to the zero power equals 1 EXPONENTS (Or POWERS are REPEATED MULTIPICATION

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google