Download presentation

Presentation is loading. Please wait.

1
**4.4 Fractional Exponents and Radicals**

2
**Construct Understanding**

3
**Construct Understanding**

4
REMEMBER Grade 9? 𝒂 𝒎 BASE

5
REMEMBER Grade 9? 𝒂 𝒎 EXPONENT

6
**𝒂 𝒎 • 𝒂 𝒏 = 𝒂 𝒎+𝒏 REMEMBER Grade 9?**

𝒂 𝒎 • 𝒂 𝒏 = 𝒂 𝒎+𝒏 We can further use it to calculate fractional exponents with numerator 1…

7
**WHAT IS A FRACTIONAL EXPONENT?**

𝒂 x y

8
**A FRACTIONAL EXPONENT with a numerator 1**

𝒂 1 y

9
**Without a calculator, Calculate**

𝟓 𝟏 𝟐 • 𝟓 𝟏 𝟐 = 𝟓 𝟏 𝟐 + 𝟏 𝟐 = 𝟓 𝟐 𝟐 = 𝟓 𝟓 • 𝟓 = 𝟐𝟓 = 𝟓 What do you notice?

10
**𝟓 𝟏 𝟐 and 𝟓 equivalent expressions**

𝟓 𝟏 𝟐 = 𝟓 𝟓 𝟏 𝟐 • 𝟓 𝟏 𝟐 = 𝟓 𝟏 𝟐 + 𝟏 𝟐 = 𝟓 𝟐 𝟐 = 𝟓 𝟓 • 𝟓 = 𝟐𝟓 = 𝟓 𝟓 𝟏 𝟐 and 𝟓 equivalent expressions

11
𝟓 𝟏 𝟐 = 𝟓 𝟓 𝟏 𝟐 • 𝟓 𝟏 𝟐 = 𝟓 𝟏 𝟐 + 𝟏 𝟐 = 𝟓 𝟐 𝟐 = 𝟓 𝟓 • 𝟓 = 𝟐𝟓 = 𝟓 Similarly,

12
**Without a calculator, Calculate**

𝟓 𝟏 𝟑 · 𝟓 𝟏 𝟑 · 𝟓 𝟏 𝟑 = 𝟓 𝟏 𝟑 + 𝟏 𝟑 + 𝟏 𝟑 = 𝟓 𝟑 𝟑 = 𝟓 𝟑 𝟓 · 𝟑 𝟓 · 𝟑 𝟓 = 𝟑 𝟏𝟐𝟓 = 𝟓 What do you notice?

13
**𝟓 𝟏 𝟑 and 𝟑 𝟓 equivalent expressions**

𝟓 𝟏 𝟑 = 𝟑 𝟓 𝟓 𝟏 𝟑 · 𝟓 𝟏 𝟑 · 𝟓 𝟏 𝟑 = 𝟓 𝟏 𝟑 + 𝟏 𝟑 + 𝟏 𝟑 = 𝟓 𝟑 𝟑 = 𝟓 𝟑 𝟓 · 𝟑 𝟓 · 𝟑 𝟓 = 𝟑 𝟏𝟐𝟓 = 𝟓 𝟓 𝟏 𝟑 and 𝟑 𝟓 equivalent expressions

14
**𝟓 𝟏 𝟐 and 𝟓 equivalent expressions**

𝟓 𝟏 𝟐 = 𝟓 𝟓 𝟏 𝟐 • 𝟓 𝟏 𝟐 = 𝟓 𝟏 𝟐 + 𝟏 𝟐 = 𝟓 𝟐 𝟐 = 𝟓 𝟓 • 𝟓 = 𝟐𝟓 = 𝟓 𝟓 𝟏 𝟐 and 𝟓 equivalent expressions

15
This suggests 𝟓 𝟏 𝟐 = 𝟓 𝟓 𝟏 𝟑 = 𝟑 𝟓 𝒙 𝟏 𝒏 = 𝒏 𝒙

16
**Powers with Rational Exponents**

𝟓 𝟏 𝟐 = 𝟓 𝟓 𝟏 𝟑 = 𝟑 𝟓 𝒙 𝟏 𝒏 = 𝒏 𝒙 When n is a natural number and x is a rational number,

17
**Evaluate each power without using a calculator**

𝟐𝟕 𝟏 𝟑 = 3 27 = 3 𝟎.𝟒𝟗 𝟏 𝟐 = 0.49 = 0.7 ( 𝟒 𝟗 ) 𝟏 𝟐 = 𝟒 𝟗 = 𝟐 𝟑

18
**POWERPOINT PRACTICE PROBLEM Evaluate each power without using a calculator**

19
**The numerator in the exponent IS NOT 1?**

What if…. The numerator in the exponent IS NOT 1? 𝟖 𝟏 𝟑 𝟖 𝟐 𝟑 𝒙 𝟏 𝒏 = 𝒏 𝒙 ??

20
RECALL.. (𝒂 𝒎 ) 𝒏 = 𝒂 𝒎 • 𝒏 So, for example,

21
𝟖 𝟐 𝟑 = 𝟖 𝟏 𝟑 · 𝟐 (𝒂 𝒎 ) 𝒏 = 𝒂 𝒎 • 𝒏 𝒂 𝒎 • 𝒏 = (𝒂 𝒎 ) 𝒏 = ( 𝟖 𝟏 𝟑 ) 𝟐 But, this is also true… = ( 𝟑 𝟖 ) 𝟐 = (𝟐) 𝟐 = 4

22
𝟖 𝟐 𝟑 = 𝟖 𝟐 · 𝟏 𝟑 (𝒂 𝒎 ) 𝒏 = 𝒂 𝒎 • 𝒏 𝒂 𝒎 • 𝒏 = (𝒂 𝒎 ) 𝒏 = ( 𝟖 𝟐 ) 𝟏 𝟑 = 𝟑 𝟖 𝟐 But, this is also true… = 𝟑 𝟔𝟒 𝒙 𝟏 𝒏 = 𝒏 𝒙 = 4

23
**Powers with Rational Exponents**

When m and n are natural numbers and x is a rational number, 𝒙 𝒎 𝒏 = ( 𝒙 𝟏 𝒏 ) 𝒎 = ( 𝒏 𝒙 ) 𝒎 𝒙 𝒎 𝒏 = ( 𝒙 𝒎 ) 𝟏 𝒏 = 𝒏 𝒙 𝒎 AND

24
**Write 𝟒𝟎 𝟐 𝟑 in radical form in 2 ways**

Write 𝟑 𝟓 and ( 𝟑 𝟐𝟓 ) 𝟐 in exponent form. 𝟒𝟎 𝟐 𝟑 = ( 𝟑 𝟒𝟎 )² and 𝟑 𝟒𝟎² 𝟑 𝟓 = 𝟑 𝟓 𝟐 ( 𝟑 𝟐𝟓 ) 𝟐 = 𝟐𝟓 𝟐 𝟑 𝒙 𝒎 𝒏 = ( 𝒙 𝟏 𝒏 ) 𝒎 = ( 𝒏 𝒙 ) 𝒎 𝒙 𝒎 𝒏 = ( 𝒙 𝒎 ) 𝟏 𝒏 = 𝒏 𝒙 𝒎

25
POWERPOINT PRACTICE PROBLEM a) Write 𝟐𝟔 𝟐 𝟓 in radical form in 2 ways b) Write 𝟔 𝟓 and ( 𝟒 𝟏𝟗 ) 𝟑 in exponent form.

26
**A husky with a body mass of 27 kg **

Biologists use the formula b = 0.01 𝒎 𝟐 𝟑 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each animal A husky with a body mass of 27 kg A polar bear with a body mass of 200g

27
**Biologists use the formula b = 0**

Biologists use the formula b = 0.01 𝒎 𝟐 𝟑 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each animal A husky with a body mass of 27 kg A polar bear with a body mass of 200g Substitute: m = 27 b = 0.01 (𝟐𝟕) 𝟐 𝟑 b = 0.01 (∛𝟐𝟕) 𝟐 b = 0.01 (𝟑) 𝟐 b = 0.09 kg The brain mass of the husky is approximately 0.09 kg.

28
**b = 0.01 (𝟐𝟎𝟎) 𝟐 𝟑 USE a CALCULATOR! Substitute: m = 200**

Biologists use the formula b = 0.01 𝒎 𝟐 𝟑 to estimate the brain mass , b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass each animal A husky with a body mass of 27 kg A polar bear with a body mass of 200g Substitute: m = 200 b = 0.01 (𝟐𝟎𝟎) 𝟐 𝟑 USE a CALCULATOR! The brain mass of the polar bear is approximately 0.34 kg.

29
**POWERPOINT PRACTICE PROBLEM Use the formula b = 0**

POWERPOINT PRACTICE PROBLEM Use the formula b = 0.01 𝒎 𝟐 𝟑 to estimate the brain mass of each animal. A moose with a body mass of 512 kg A cat with a body mass of 5 kg

30
Section 4.4 HOMEWORK PAGES: 227 – 228 PROBLEMS:

31
QUIZ Sections 4.1 – 4.3 Friday, July 25

Similar presentations

OK

Section 6-2 Day 1 Apply Properties of Rational Exponents.

Section 6-2 Day 1 Apply Properties of Rational Exponents.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on trial and error factoring Ppt on statistics and probability questions Ppt on economic order quantity equation Ppt on aircraft landing gear system description Ppt on ip address classes table Ppt on direct tax code bill Ppt on leadership in nursing Ppt on high voltage engineering corp Ppt on hindu religion pictures Ppt on green building design