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प्रश्न
By what number should \[\left( \frac{5}{3} \right)^{- 2}\] be multiplied so that the product may be \[\left( \frac{7}{3} \right)^{- 1} ?\]
उत्तर
Expressing as a positive exponent, we have:
`(5/3)^(-2)=1/(5/3)^2` → (a−1 = 1/a)
`=1/(25/9)` → ((a/b)n = (an)/(bn))
and
(7/3)−1 = 3/7. → (a−1 = 1/a)
We have to find a number x such that
`9/25xx x=3/7`
Multiplying both sides by 25/9, we get:
`x=3/7xx25/9=1/7xx25/3=25/21`
Hence, (5/3)−2 should be multiplied by 25/21 to obtain (7/3)−1.
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संबंधित प्रश्न
Simplify and express the result in power notation with positive exponent.
`(1/2^3)^2`
By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( - \frac{4}{7} \right)^{- 1} ?\]
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5−2
Simplify:
By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( \frac{- 4}{7} \right)^{- 1} ?\]
Cube of \[\frac{- 1}{2}\] is
For a non zero rational number a, (a3)−2 is equal to
The multiplicative inverse of (– 4)–2 is (4)–2.
Predicting the ones digit, copy and complete this table and answer the questions that follow.
| 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
- 10500
- Predict the ones digit in the following:
- 3110
- 1210
- 1721
- 2910
