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प्रश्न
Simplify:
(25 ÷ 28) × 2–7
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उत्तर
Using laws of exponents,
am ÷ an = (a)m – n and am × an = (a)m + n ...[∵ a is non-zero integer]
∴ (25 ÷ 28) × (2)–7 = (2)5 – 8 × (2)–7
= (2)–3 × (2)–7
= (2)–3 – 7
= (2)–10
= `1/2^10` ...`[∵ a^-m = 1/a^m]`
= `1/1024`
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am × bm = (ab)m
Find a single repeater machine that will do the same work as hook-up.

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 | |||
If a = – 1, b = 2, then find the value of the following:
ab ÷ ba
