Question

The value of ${\left(16\right)}^{1/4}$ are

• A. $\pm 2,\pm 2i$
• B. $\pm 4,\pm 4i$
• C. $\pm 1,\pm i$
• D. None of these

Answer 1

The correct option is A $\pm 2,\pm 2i$

Let $x={\left(16\right)}^{1/4}$
$x^4=16$
$x^4-16=0$
$x^4-2^4=0$
$(x^2-2^2)(x^2+2^2)=0$
$(x-2)(x+2)(x^2+4)=0$
$x-2=0,x+2=0,x^2+4=0$
$x=2,-2$ or $x^2=-4⟹x=\pm \sqrt{-4}=\pm 2i$
$\therefore x=\pm 2,\pm 2i$