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Question
Find the value of (2−1 × 4−1) ÷2−2.
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Solution
`(2^(−1) × 4^(−1)) ÷ 2^(−2)`
= `[2^-1 xx (2^-2)^-1] ÷ 2^-2`
= `[2^-1 xx 2^-2]÷ 2^-2` ...[∵ (am)n = amn]
= `[2^(-1 + (-2))]÷2^-2` ...[∵ am × an = am+n]1
= `[2^(-1-2) ÷ 2^-2]`
= `2^-3 ÷ 2^-2`
= `2^(-3 - (-2))` .....[∵ am ÷ an = am−n]
= 2−3+2 = 2−1
= `1/2`
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