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Question
Find the value of m for which 5m ÷5−3 = 55.
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Solution
5m ÷ 5−3 = 55
`5^(m-(-3)) = 5^5` ... [am÷ an = am-n]
5m + 3 = 55 ...[∵ am = an ⇒ m = n]
Since the powers have the same bases on both sides, their respective exponents must be equal.
m + 3 = 5
m = 5 − 3
m = 2
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