[] is the square root of 10-6.

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

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

let x=$\sqrt{{10}^{-6}}$
x=${\left({10}^{-6}\right)}^{\frac{1}{2}}$
Here, the base is 10 and the indices are −6 and .
We know that, the power of a power property states that${\left({a}^{b}\right)}^{c}$=${a}^{\left(b×c\right)}$
So, simplifying x accordingly, we get,
X = ${10}^{\left(\left(-6\right)×\left(\frac{1}{2}\right)\right)}$
⇒x=${10}^{\left(-3\right)}$
Now, we know that negative powers are nothing but the power of the reciprocal of the base number. In other words,
${a}^{\left(-b\right)}$= $\frac{1}{{a}^{b}}$ Simplifying x according to this rule, we get,
X = ${10}^{\left(-3\right)}$
⇒x =  $\frac{1}{{10}^{3}}$
We know that
= 1000
Thus,
X =
x=0.001

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)