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Question
Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.
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Solution
We know that
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Simplify:
\[\left( 3^{- 1} \times 4^{- 1} \right)^{- 1} \times 5^{- 1}\]
Evaluate:
5−2
Express the following as a rational number in the form \[\frac{p}{q}:\]
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
if \[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}\], find the value of x−2.
Find the value of x for which 52x ÷ 5−3 = 55.
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.
2−3 × (−7)−3
