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Question
`(11/15)^4 xx (_)^5 = (11/15)^9`
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Solution
`(11/15)^4 xx underlinebb((11/15))^5 = (11/15)^9`
Explanation:
Let `(11/15)^4 xx (x)^5 = (11/15)^9`
⇒ `(x)^5 = (11/15)^9/(11/15)^4`
⇒ `(x)^5 = (11/15)^9 (11/15)^-4`
⇒ `(x)^5 = (11/15)^(9 - 4)` ...`[∵ a^m xx a^-n = a^(m + (-n)) = a^(m - n)]`
⇒ `(x)^5 = (11/15)^5`
Since, the powers are same.
∴ `x = 11/15`
Hence, `(11/15)^4 xx (11/15)^5 = (11/15)^9`
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