## anonymous one year ago check attachments please? thanks!

1. anonymous

2. mathstudent55

Problem 1. Do you know the definition of a rational (fraction) exponent?

3. anonymous

@mathstudent55 im afraid i don't

4. mathstudent55

$$\Huge a^{\frac{m}{n}} = \sqrt[n] {a^m} = (\sqrt[n]a)^m$$

5. mathstudent55

To find a rational power of a number, raise the number to the numerator of the exponent and take the root of the number the denominator tells you.

6. mathstudent55

Keep in mind: numerator -------> exponent denominator -----> root

7. mathstudent55

Examples: |dw:1438493658565:dw|

8. mathstudent55

|dw:1438493695962:dw|

9. mathstudent55

|dw:1438493741614:dw|

10. mathstudent55

Do you understand the examples?

11. mathstudent55

All the examples show you the same idea. The denominator of the exponent tells you which root to take. When the denominator is 2, you take the square root. When the denominator is 3 you take the cubic root, etc.

12. mathstudent55

The numerator tells you what power to raise the number to before or after you take the root.

13. anonymous

yes. i do. what i don't get is that when you get the result you get a single number, but my answer choices have the square root symbol would what you showed me still apply?

14. mathstudent55

Let's look at problem 1 now together.

15. mathstudent55

|dw:1438494095419:dw|

16. mathstudent55

What does the 2 in the denominator mean?

17. anonymous

numerator?

18. mathstudent55

From above: "The denominator of the exponent tells you which root to take."

19. mathstudent55

"When the denominator is 2, you take the square root. "

20. mathstudent55

A denominator of 2 means take the square root. |dw:1438494212377:dw|

21. mathstudent55

The numerator of 3 means raise the number to the 3rd power.

22. mathstudent55

What is $$2^3$$ equal to?

23. anonymous

8. but what do you do with the denominator in the fraction?

24. mathstudent55

|dw:1438494329059:dw|

25. mathstudent55

The denominator of the exponent changed the problem from an exponent problem to a root problem.

26. mathstudent55

|dw:1438494376526:dw|

27. anonymous

OOHHHHHHHHHH OMG IM SO STUPIDDDD LOL

28. mathstudent55

No, you're not stupid. You're learning. I went through the same process you are going through now.

29. mathstudent55

Are you ready for problem 2?

30. anonymous

yup

31. mathstudent55

Here you will need a property of exponents. Here it is: $$\Huge \dfrac{a^m}{a^n} = a^{m - n}$$ When you divide powers with the same base, write the same base and subtract the exponents.

32. mathstudent55

Here is an example of this rule: |dw:1438494620860:dw| Do you underrstand the example?

33. anonymous

yes

34. mathstudent55

OK. Now lets do problem 2.

35. mathstudent55

The first step is to use the rational exponents in reverse. Earlier, I explained how to handle a fraction as an exponent. In this problem, you are given a root in the numerator and a root in the denominator. We need to use the rule of rational exponents in reverse, and write the numerator and denominator of this fraction with fractions for the exponents.

36. mathstudent55

Let's just look at the numerator of our problem.

37. mathstudent55

|dw:1438494930324:dw|

38. mathstudent55

|dw:1438495081620:dw| We need to replace the box with an exponent. You need to work backwards, and figure out what fraction you need to raise 7 to to get the cubic root of 7. Remember above we saw that the denominator of an exponent tells you which root to take. Here we see we are taking the 3rd root (called the cubic root) of 7. If we take the cubic root of 7, what do we need in the denominator of the exponent?

39. anonymous

3?

40. mathstudent55

|dw:1438495150225:dw|

41. mathstudent55

Exaclty. Also, since we have just 7, not 7 raised to some power, that means the numerator is 1.

42. mathstudent55

|dw:1438495224736:dw|

43. mathstudent55

|dw:1438495237856:dw| Ok?

44. anonymous

alright

45. mathstudent55

Now let's look at the denominator. The denominator is similar to the numerator except instead of the cubic root, it's the fifth root.

46. mathstudent55

|dw:1438495324943:dw| What fraction is the exponent of 7?

47. mathstudent55

|dw:1438495375343:dw|

48. anonymous

|dw:1438495456106:dw| would this be it?

49. mathstudent55

Correct. Now let's put it together the way the problem is given. |dw:1438495483142:dw|

50. mathstudent55

Now you need the rule I gave you above. What do you do when you dived powers with the same base? You subtract the exponents. |dw:1438495589942:dw| What goes in the box?

51. anonymous

2/15 ?

52. mathstudent55

|dw:1438495725285:dw|

53. mathstudent55

Correct.

54. anonymous

thank you! can you help me with 1 last question?

55. mathstudent55

You're welcome. Sure, one more.

56. anonymous

57. mathstudent55

Have you learned how to solve systems of equations by the addition method?

58. anonymous

im afraid not

59. anonymous

wouldn't the value of y be 8?

60. mathstudent55

We need to solve the system.

61. anonymous

wait i got this question. i sent the wrong picture wow

62. mathstudent55

Have you learned how to solve a system of equations by the substitution method?

63. anonymous

this was the one

64. anonymous

@mathstudent55 well turns out i did because in the snapshot there was no answer. but then i check on my page and it had the answer on it, so i probably figured out this morning

65. mathstudent55

Ok. I see.

66. mathstudent55

The graph of $$y = \sqrt x$$ looks like this: |dw:1438496300889:dw|

67. mathstudent55

When you replace x by x - k, where k is a number, the graph shifts horizontally (left or right) k units.

68. mathstudent55

|dw:1438496428565:dw|

69. mathstudent55

If you compare $$y = \sqrt x$$ with $$y = \sqrt{x + 7}$$, you see that x was replaced by x + 7. That means that when you compare x + 7 with x - k, you see that it equals x - (-7). k = -7. Since k is a negative number, it means the graph shifts to the left. The 7 tells you it is a shift of 7 units left.

70. mathstudent55

|dw:1438496631995:dw|

71. anonymous

b and d are giving me some strong feelings for some reason. both of them feel right

72. mathstudent55

From the graphs of the choices, you see that: B is shifted 6 units left D is shifted 7 units left.

73. anonymous

d?

74. anonymous

@arindameducationusc do you know what the answer would be??

75. arindameducationusc

For question 1, 3 is for square power and 2 is for square root power... so apply that

76. anonymous

@arindameducationusc im afraid i have already answered question 1. I'm sorry for not informing you . i need 2

77. arindameducationusc

Just follow mathstudent steps... He is right