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प्रश्न
Find the value of the following:
(30 + 4−1) × 22
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उत्तर
We know from the property of powers that for every natural number a, a−1 = 1/a.
Moreover, a0 is 1 for every natural number a not equal to 0. Then:
\[\left( 3^0 + 4^{- 1} \right) \times 2^2 \]
\[ = \left( 1 + \frac{1}{4} \right) \times 4 \left[ as, a^{- 1} = \frac{1}{a}; a^0 = 1 \right]\]
\[ = \frac{5}{4} \times 4\]
\[ = 5\]
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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 | ||||||||
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