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Question
Find the value of x so that `(5/3)^-2 xx (5/3)^-14 = (5/3)^(8x)`
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Solution
We have, `(5/3)^-2 xx (5/3)^-14 = (5/3)^(8x)`
Using law of exponents,
am × an = (a)m + n ...[∵ a is non-zero integer]
Then, `(5/3)^-2 xx (5/3)^-14 = (5/3)^(8x)`
⇒ `(5/3)^(-2 - 14) = (5/3)^(8x)`
⇒ `(5/3)^(-16) = (5/3)^(8x)`
On comparing both sides, we get
16 = 8x
⇒ x = – 2
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