Comparing exponent expressions — Transcript

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1. 0:00So, we are asked to order the
2. 0:02expressions from least to greatest. And
3. 0:04this is from the exercises on Khan
4. 0:06Academy. And if we're doing it on Khan
5. 0:08Academy, we would drag these little
6. 0:10tiles around from least to greatest.
7. 0:13Least on the left, greatest on the
8. 0:14right. I can't drag it around cuz this
9. 0:16is just a picture. So, I'm going to
10. 0:17evaluate each of these, and then I'm
11. 0:19going to rewrite them from least to
12. 0:20greatest. So, let's start with 2 to the
13. 0:23third minus 2 to the first. What is that
14. 0:25going to be? 2 to the third minus 2 to
15. 0:27the first. And if you feel really
16. 0:28confident, just pause this video and try
17. 0:29to figure out the whole thing. Order
18. 0:31them from least to greatest.
19. 0:33Well, 2 to the third, that is 2 * 2 * 2.
20. 0:37And then 2 to the first, well, that's
21. 0:39just 2.
22. 0:40So, 2 * 2 is 4 * 2 is 8 - 2.
23. 0:45This is going to be equal to 6. So, this
24. 0:48expression right over here could be
25. 0:50evaluated as being equal to 6.
26. 0:52Now, what about this right over here?
27. 0:55What is this equal to?
28. 0:57Well, let's see. We have 2 squared + 3
29. 1:02to the 0. 2 squared is 2 * 2.
30. 1:06And anything to the 0 power is going to
31. 1:10be equal to 1. The interesting thing to
32. 1:12think about what 0 to the 0 power should
33. 1:14be, but that'll be a topic for another
34. 1:16video. But here we have 3 to the 0
35. 1:18power, which is clearly equal to 1. And
36. 1:22so, we have 2 * 2 + 1. This is 4 + 1,
37. 1:25which is equal to 5. So, the second tile
38. 1:28is equal to 5.
39. 1:30And then 3 squared. Well, 3 squared,
40. 1:33that's just 3 * 3. 3 * 3 is equal to 9.
41. 1:39So, if I were to order them from least
42. 1:40to greatest, the smallest of these is
43. 1:442 squared + 3 to the 0 power. That one
44. 1:47is equal to 5, so I'll put that on the
45. 1:49left. Then we have this thing that's
46. 1:52equal to 6, 2 to the third power minus 2
47. 1:54to to first power.
48. 1:56And then the largest value here is 3
49. 1:59squared.
50. 2:00So, we would put that tile 3 squared, we
51. 2:04will put that tile on the right. And
52. 2:06we're done.