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Question
For hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.
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Solution
Using law of exponents,
am × an = (a)m + n ...[∵ a is non-zero integer]
Hook-up machine can do the work = 23 × 32 = 8 × 9 = 72
So, it is not possible for a single machine to do the same work.
Since, (× 82) = 64 and (× 92) = 81
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Simplify:
`(((-2)/3)^-2)^3 xx (1/3)^-4 xx 3^-1 xx 1/6`
What happens when 1 cm worms are sent through these hook-ups?
Find a single machine that will do the same job as the given hook-up.
a (× 23) machine followed by (× 2–2) machine.
Find a single repeater machine that will do the same work as hook-up.
If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.
The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
| Input Length | Repeater Machine | ||
| × 23 | |||
| 40 | 125 | ||
| 2 | |||
| 162 | |||
Simplify:
`((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`
