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Question
By what number should `((-3)/2)^-3` be divided so that the quotient may be `(4/27)^-2`?
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Solution
Let `((-3)/2)^-3` be divided by x to get `(4/27)^-2` as quotient.
Then, `((-3)/2)^-3 ÷ x = (4/27)^-2`
⇒ `x = ((-3)/2)^-3 ÷ (2^2/3^3)^-2 = ((-3)/2)^-3 ÷ (2)^-4/(3)^-6`
= `((-3)/2)^-3 xx (3)^-6/(2)^-4`
= `((-3)^-3 xx (3)^-6)/(2^-3 xx 2^-4` ...[∵ am × an = am + n]
= `3^-9/2^-7`
= `2^7/3^9` ...`[∵ a^-m = 1/a^m "and" (a^m)^n = (a)^(mn)]`
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