Question

Find m so that `(2/9)^3 xx (2/9)^6 = (2/9)^(2m - 1)`

Answer 1

We have `(2/9)^3 xx (2/9)^6 = (2/9)^(2m - 1)`

⇒ `(2/9)^(3 + 6) = (2/9)^(2m - 1)`  ...[∵ a^m × aⁿ = a^{m + n}]

⇒ `(2/9)^9 = (2/9)^(2m - 1)`

⇒ 9 = 2m – 1  ...[∵ a^m = 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.