What is sqrt(-1)sqrt(-1)sqrt(-1)sqrt(-1) ?

The solution to sqrt(-1)sqrt(-1)sqrt(-1)sqrt(-1) is 1

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simplify sqrt(-1)sqrt(-1)sqrt(-1)sqrt(-1)

simplify

- 1 - 1 - 1 - 1

1

Solution steps

- 1 - 1 - 1 - 1

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

- 1 - 1 - 1 - 1 = (- 1)^{\frac{1}{2}} (- 1)^{\frac{1}{2}} (- 1)^{\frac{1}{2}} (- 1)^{\frac{1}{2}} = (- 1)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

= (- 1)^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Combine the fractions

\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} : 2

= (- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

e^{- 2 x^{2}} d x

e^{- x^{- a}}

- e^{- t^{2}}

e^{x} \cdot (- 2) e^{- 2 x}

e^{j x} \cdot e^{j x}

What is sqrt(-1)sqrt(-1)sqrt(-1)sqrt(-1) ?
The solution to sqrt(-1)sqrt(-1)sqrt(-1)sqrt(-1) is 1