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Question
Find the value of n.
`(2^n xx 2^6)/2^-3 = 2^18`
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Solution
Given, `(2^n xx 2^6)/2^-3 = 2^18`
Using law of exponents,
`a^-m = 1/a^m` ...[∵ a is non-zero integer]
⇒ 2n × 26 × 23 = 218
⇒ 2n + 9 = 218 ...[∵ am × an = am + n]
On comparing both sides, we get
n + 9 = 18 ...[∵ am ÷ an = (a)m – n]
⇒ n = 9
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