Question

`((-3)/5)^100 = (-3^100)/(-5^100)`

Options

• True

• False

Answer 1

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 = a^m × b^m]

= `(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)`