Question

simplify the given expression to rational exponet form justify each step by identifying the properities of rational exponents used 1/ 3sqrt x^-6

Answer 1

\[1/(3\sqrt{x^{-6}}) = 1/(3x^{-3})\] because the square root of x is the same as taking it to the .5 power, and when you take it by 2 powers you mutiply them to get that x^-3
\[x^{-3}=1/x^{3}\]
\[1/(3\frac{ 1 }{ x^{3} })=x^{3}/3\]
I'm not sure if you were asking 1/(3sqrt x^-6) or 1/3 (sqrt x^-6) or 1/3 (sqrt x)^-6 so I just sort of assumed but I hope that helps!