If $x^{2}+frac{1}{x^{2}}=2$, then what is the value of $x^{6} ?$

$x^{2}+frac{1}{x^{2}}=2$

$Rightarrow x^{4}+1=2 x^{2}$

$Rightarrow x^{4}-2 x^{2}+1=0$

$Rightarrowleft(x^{2}-1 ight)^{2}=0$

$Rightarrow x^{2}-1=0 Rightarrow x^{2}=1$

$herefore x^{6}=1$