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Question
Find m so that `(2/9)^3 xx (2/9)^6 = (2/9)^(2m - 1)`
Solution
We have `(2/9)^3 xx (2/9)^6 = (2/9)^(2m - 1)`
⇒ `(2/9)^(3 + 6) = (2/9)^(2m - 1)` ......[∵ am × an = am+n]
⇒ `(2/9)^9 = (2/9)^(2m - 1)`
⇒ 9 = 2m – 1 ......[∵ am = an ⇒ m = n]
⇒ 9 + 1 = 2m ......[Transposing (–1) to LHS]
⇒ 10 = 2m
⇒ `10/2 = (2m)/2` ......[Dividing both sides by 2]
⇒ 5 = m
Hence, m = 5.
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