Lesson 8 of 14
Which of two powers is larger
Show on a big screenWhich is larger, 2¹⁰ or 10³? Ten 2s multiplied, against three 10s multiplied.
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2¹⁰ — ten 2s multiplied. Step 1 of 4
2¹⁰— ten 2s multiplied.2¹⁰= 1024.10³— three tens multiplied.10³= 1000.2¹⁰wins.
The rule
2¹⁰ is larger. It is 1024, and 10³ is 1000.
Same base above 1? The bigger count wins. Same count above 0? The bigger base wins. Neither the same? Work both out. With a base above 1, each extra copy makes the number bigger.
In the table, neither shortcut alone is right for every pair.
| Pair | Values | Larger | Bigger base says | Bigger count says |
|---|---|---|---|---|
| 2¹⁰ and 10³ | 1024, 1000 | 2¹⁰ | 10³, wrong | 2¹⁰, right |
| 3² and 2³ | 9, 8 | 3² | 3², right | 2³, wrong |
| 5³ and 3⁵ | 125, 243 | 3⁵ | 5³, wrong | 3⁵, right |
| 2⁴ and 4² | 16, 16 | tie | 4², wrong | 2⁴, wrong |
Try the lab to finish this lesson.