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Question
`((-3)/5)^100 = (-3^100)/(-5^100)`
Options
True
False
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Solution
This statement is True.
Explanation:
Taking LHS, we have
`((-3)/5)^100 = ((-1 xx 3)/5)^100` ...[∵ –3 = –1 × 3]
= `((-1)^100 xx 3^100)/5^100` ...[∵ (a × b)m = am × bm]
= `(1 xx 3^100)/5^100` ...[∵ (–1)n = 1, if n is even]
= `3^100/5^100`
Now, taking RHS, we have
`(-3^100)/(-5^100) = 3^100/5^100` ...`[(∵ "If both numerator and denominator have"),("negative sign, then it is cancelled out")]`
∴ LHS = RHS
Hence, `(-3^100)/5 = (-3^100)/(-5^100)`
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