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Question
Which of the following is not reciprocal of \[\left( \frac{2}{3} \right)^4 ?\]
Options
- \[\left( \frac{3}{2} \right)^4\]
- \[\left( \frac{2}{3} \right)^{- 4}\]
- \[\left( \frac{3}{2} \right)^{- 4}\]
- \[\frac{3^4}{2^4}\]
MCQ
Sum
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Solution
\[\left( \frac{3}{2} \right)^{- 4}\]
The reciprocal of `(2/3)^4` is `(3/2)^4`
Therefore, option (a) is the correct answer.
Option (b) is just re-expressing the number with a negative exponent.
Option (d) is obtained by working out the exponent.
Hence,option (c) is not the reciprocal of `(2/3)^4`.
The reciprocal of `(2/3)^4` is `(3/2)^4`
Therefore, option (a) is the correct answer.
Option (b) is just re-expressing the number with a negative exponent.
Option (d) is obtained by working out the exponent.
Hence,option (c) is not the reciprocal of `(2/3)^4`.
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| Powers Table | ||||||||||
| x | 1x | 2x | 3x | 4x | 5x | 6x | 7x | 8x | 9x | 10x |
| 1 | 1 | 2 | ||||||||
| 2 | 1 | 4 | ||||||||
| 3 | 1 | 8 | ||||||||
| 4 | 1 | 16 | ||||||||
| 5 | 1 | 32 | ||||||||
| 6 | 1 | 64 | ||||||||
| 7 | 1 | 128 | ||||||||
| 8 | 1 | 256 | ||||||||
| Ones Digits of the Powers |
1 | 2, 4, 8, 6 | ||||||||
- Describe patterns you see in the ones digits of the powers.
- Predict the ones digit in the following:
- 412
- 920
- 317
- 5100
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- 3110
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Simplify and express the result in power notation with positive exponent.
`(−3)^4 × (5/3)^4`
