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Question
`((-1)/4)^3 xx ((-1)/4)^- = ((-1)/4)^11`
Solution
`((-1)/4)^3 xx ((-1)/4)^bb(underline(8)) = ((-1)/4)^11`
Explanation:
Let `((-1)/4)^3 xx ((-1)/4)^x = ((-1)/4)^11`
⇒ `((-1)/4)^x = ((-1)/4)^11/((-1)/4)^3`
⇒ `((-1)/4)^x = ((-1)/4)^(11-3)` ......[∵ am ÷ an = am–n, m > n]
⇒ `((-1)/4)^x = ((-1)/4)^8`
Since, base are equal. So, by equating the powers, we get x = 8
∴ `((-1)/4)^3 xx ((-1)/4)^8 = ((-1)/4)^11`
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