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[[1]] is the square root of $10^{- 6}$ .

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Detailed Solution

let x=

\sqrt{10^{- 6}}

{(10^{- 6})}^{\frac{1}{2}}

Here, the base is 10 and the indices are −6 and

\frac{1}{2}

.
We know that, the power of a power property states that

{(a^{b})}^{c}

a^{(b \times c)}

So, simplifying x accordingly, we get,
X =

10^{((- 6) \times (\frac{1}{2}))}

⇒x=

10^{(- 3)}

Now, we know that negative powers are nothing but the power of the reciprocal of the base number. In other words,

a^{(- b)}

\frac{1}{a^{b}}

Simplifying x according to this rule, we get,
X =

10^{(- 3)}

⇒x =

\frac{1}{10^{3}}

We know that

10^{3}

= 1000
Thus,
X =

\frac{1}{1000}

x=0.001

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