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प्रश्न
Express the following rational numbers with a positive exponent:
उत्तर
\[4^3 \times 4^{- 9} \]
\[ = 4^\left( 3 - 9 \right) = 4^{- 6} \]
\[ = \left( \frac{1}{4} \right)^6\] → (am x an = am+n)
APPEARS IN
संबंधित प्रश्न
Find the value of the following:
\[\left\{ \left( \frac{1}{3} \right)^{- 1} - \left( \frac{1}{4} \right)^{- 1} \right\}^{- 1}\]
Simplify:
By what number should \[\left( \frac{5}{3} \right)^{- 2}\] be multiplied so that the product may be \[\left( \frac{7}{3} \right)^{- 1} ?\]
Find x, if
Square of \[\left( \frac{- 2}{3} \right)\] is
The multiplicative inverse of `(3/2)^2` is not equal to `(2/3)^-2`.
Express 3–5 × 3–4 as a power of 3 with positive exponent.
Express 16–2 as a power with the base 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
Simplify and express the result in power notation with positive exponent.
`(−3)^4 × (5/3)^4`
