Question

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

Answer 1

We want to simplify the expression

`\frac{1}{x^{(-(3)/(6))}}`

First we will simplify the exponent:

`-(3)/(6)\rightarrow-(1)/(2)`

So now we have

`\frac{1}{x^{(-(1)/(2))}}`

Next, we need to apply the negative exponent property, which states that for any positive value of m and n,

`(1)/(m^(-n))\rightarrow m^n`

(We flip the fraction to the its reciprocal, then change the sign of the exponent.)

Our new expression is:

`x^{(1)/(2)}`

Finally, we need to apply the rational exponent rule. Which states for any positive integer value of m and n,

`x^{(m)/(n)}=\sqrt[n]{x^m}`

Notice the n becomes the index of the radical, and the m becomes the power of the number under the radical.

So, we have

`\sqrt[2]{x}^1\rightarrow√(x)`

Our final answer is

`\boxed{√(x)}`