Question

(-1)×(-1)^2×(-1)^3×(-1)^1/4×....×(-1)14

Answer 1

Я так полагаю, что (-1)⁴, а не (-1)^-¼

(-1)×(-1)²×(-1)³×(-1)⁴×...×(-1)¹³×(-1)¹⁴=
=(-1)×(1)×(-1)×(1)×...(-1)×1=
=[(-1)×(1)]×[(-1)×(1)]×...[(-1)×1]
разбили на пары , всего таких пар 14/2=7
=(-1)^7= -1

Answer 2

Let's simplify the expression step by step:

1. (-1) × (-1)^2 = (-1) × 1 = -1
2. (-1)^3 = -1
3. (-1)^1 = -1

Now, let's handle the fractional exponent, (-1)^(1/4). The fourth root of -1 can be expressed as a complex number since there is no real number that satisfies this condition. The fourth roots of -1 are: 1, -1, i, and -i. Thus, (-1)^(1/4) can be either 1, -1, i, or -i.

Next, we encounter (-1)^14, which is equal to 1.

Now, let's put everything together:

(-1) × (-1)^2 × (-1)^3 × (-1)^1/4 × .... × (-1)^14

= -1 × (-1) × (-1) × (-1)^1/4 × .... × 1

= -1 × (-1)^1/4 × .... × 1

At this point, we need to consider the value of (-1)^1/4. As mentioned earlier, (-1)^1/4 can be either 1, -1, i, or -i. So, we have four possibilities for the final result:

1. If (-1)^1/4 = 1, then the expression becomes: -1 × 1 × 1 × .... × 1 = -1
2. If (-1)^1/4 = -1, then the expression becomes: -1 × -1 × 1 × .... × 1 = 1
3. If (-1)^1/4 = i, then the expression becomes: -1 × i × 1 × .... × 1 = -i
4. If (-1)^1/4 = -i, then the expression becomes: -1 × -i × 1 × .... × 1 = i

So, depending on the value of (-1)^1/4, the final result can be -1, 1, -i, or i.