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प्रश्न
Simplify and express the result in power notation with positive exponent.
(−4)5 ÷ (−4)8
सरल रूप दीजिए
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उत्तर
We have, (−4)5 ÷ (−4)8
= (−4)5-8
= (−4)−3
= `1/(-4)^3` ....`[∵ a^m ÷ a^n = a^(m-n), a^-m = 1/a^m]`
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अध्याय 10: Exponents and Powers - EXERCISE 10.1 [पृष्ठ १२५]
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संबंधित प्रश्न
Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.
\[\left( \frac{1}{2} \right)^{- 5}\]
Find the value of the following:
\[\left\{ \left( \frac{1}{3} \right)^{- 1} - \left( \frac{1}{4} \right)^{- 1} \right\}^{- 1}\]
Simplify:
\[\left( 5^{- 1} \div 6^{- 1} \right)^3\]
Simplify:
\[\left( 2^2 + 3^2 - 4^2 \right) \div \left( \frac{3}{2} \right)^2\]
Express the following rational numbers with a negative exponent:
\[\left( \frac{1}{4} \right)^3\]
Express the following rational numbers with a positive exponent:
\[\left\{ \left( \frac{4}{3} \right)^{- 3} \right\}^{- 4}\]
Cube of \[\frac{- 1}{2}\] is
\[\left( \frac{2}{3} \right)^{- 5} \times \left( \frac{5}{7} \right)^{- 5}\] is equal to
Find the multiplicative inverse of the following.
10– 100
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
