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प्रश्न
Simplify:
\[\left( 2^2 + 3^2 - 4^2 \right) \div \left( \frac{3}{2} \right)^2\]
बेरीज
उत्तर
\[( 2^2 + 3^2 - 4^2 ) \div \left( \frac{3}{2} \right)^2 = (4 + 9 - 16) \times \frac{9}{4}\] `->((a/b)^n=(a^n)/(b^n))`
\[= - 3 \times \frac{4}{9}\] ...(We know that `1/a div 1/b = 1/a xx b/1`)
`-4/3`
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संबंधित प्रश्न
Evaluate.
(−4)−2
Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.
\[\left( \frac{1}{2} \right)^{- 5}\]
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(3−1 + 4−1 + 5−1)0
Simplify:
\[\left[ \left( \frac{1}{3} \right)^{- 3} - \left( \frac{1}{2} \right)^{- 3} \right] \div \left( \frac{1}{4} \right)^{- 3}\]
By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?
Find x, if
\[\left( \frac{- 1}{2} \right)^{- 19} \times \left( \frac{- 1}{2} \right)^8 = \left( \frac{- 1}{2} \right)^{- 2x + 1}\]
Find x, if
\[\left( \frac{2}{5} \right)^{- 3} \times \left( \frac{2}{5} \right)^{15} = \left( \frac{2}{5} \right)^{2 + 3x}\]
Find x, if
\[\left( \frac{5}{4} \right)^{- x} \div \left( \frac{5}{4} \right)^{- 4} = \left( \frac{5}{4} \right)^5\]
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
