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Question
If `(5^m xx 5^3 xx 5^-2)/5^-5 = 5^12`, find m.
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Solution
Given, `(5^m xx 5^3 xx 5^-2)/5^-5 = 5^12`
Using laws of exponents,
am + an = (a)m – n and `a^-m = 1/a^n` ...[∵ a is non-zero integer]
Then, 5m × 53 × 5–2 × 55 = 512
⇒ 5m × 58 × 5–2 = 512
⇒ 5m × 56 = 512
⇒ 5m + 6 = 1512 ...[∵ am × an = am + n]
On comparing both sides, we get
m + 6 = 12
⇒ m = 6
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