Question 114539
1.
{{{3^sqrt(-27)= 3^(sqrt(27)sqrt(-1))= 3^(3i)}}}

2.

{{{sqrt((-3x)^2) = -3x}}}

3.

{{{sqrt(-4) = sqrt(4)*sqrt(-1) = 2i}}}…………. imaginary number {{{i*i = -1}}}

4.

{{{3^sqrt(-(1/8))}}}……………….. apply rule {{{sqrt(a/b) = sqrt(a)/sqrt(b)}}} 

where {{{b}}} cannot be equal to {{{0}}}



{{{3^(sqrt(-1)/sqrt(8))=3^(i/sqrt(8))}}}………… {{{sqrt(-1)=i}}}



Since {{{sqrt(8)=2.8284271247461903=2.83}}}, we will have:



{{{3^(sqrt(-1)/sqrt(8)) = 3^(i/2.83)}}}…………