Question

Rewrite in simplest radical form
1 over x^-3/6
Show each step of your process.

Answer 1

`\frac{1}{x^{-(3)/(6)}}\\------------------\\-(3)/(6)=-(3:3)/(6:3)=-(1)/(2)\\\\use:\\\\(1)\ \left((1)/(a)\right)^n=(1)/(a^n)\\\\(2)\ a^(-n)=\left((1)/(a)\right)^n\\\\(3)\ a^(1)/(n)=\sqrt[n]{a}`


`\frac{1}{x^{-(3)/(6)}}=\frac{1}{x^{-(1)/(2)}}\to(1)\to\left((1)/(x)\right)^{-(1)/(2)}\to(2)\to\left((x)/(1)\right)^(1)/(2)=x^(1)/(2)\to(3)\to\boxed{\boxed{\sqrt[2]{x}=√(x)}}`


`Domain:\\x\\eq0\ and\ x\geq 0\Rightarrow x \ \textgreater \ 0\to x\in(0;\ \infty)`