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Question
A student said that `3^5/9^5` is the same as `1/3`. What mistake has the student made?
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Solution
We have, `3^5/9^5 = 3^5/(3^2)^5` ...[∵ 9 = 3 × 3 = 32]
= `3^5/3^10` = `1/(3^(10 - 5)` = `1/3^5` ...`[∵ a^m/a^n = a^(m - n)]`
So, `1/3` is not same as `1/3^5`
Student has multiplied the base by its exponent.
This is the error.
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