Question

Rewrite in simplest radical form 1 over the quantity x to the negative three sixths end quantity. Show each step of your process.

Answer 1

To rewrite \( \frac{1}{x^{-\frac{3}{6}}} \) in simplest radical form, we will follow these steps:

1. **Simplify the exponent:**
The exponent \(-\frac{3}{6}\) can be simplified:
\[
-\frac{3}{6} = -\frac{1}{2}
\]
Thus, we can rewrite the expression as:
\[
\frac{1}{x^{-\frac{1}{2}}}
\]

2. **Change the negative exponent:**
Recall that for any base \(a\), \(a^{-b} = \frac{1}{a^b}\). Therefore, we can rewrite \(x^{-\frac{1}{2}}\):
\[
x^{-\frac{1}{2}} = \frac{1}{x^{\frac{1}{2}}}
\]
So, our expression becomes:
\[
\frac{1}{\frac{1}{x^{\frac{1}{2}}}} = x^{\frac{1}{2}}
\]

3. **Convert to radical form:**
The exponent \(\frac{1}{2}\) corresponds to the square root. Thus, we rewrite it as:
\[
x^{\frac{1}{2}} = \sqrt{x}
\]

Finally, we conclude that:
\[
\frac{1}{x^{-\frac{3}{6}}} = \sqrt{x}
\]

So the answer in simplest radical form is \( \sqrt{x} \).