Question

How do you write $ 2{x^{ - \dfrac{1}{2}}} $ in radical form?

Answer 1

Hint: Take the given expression and simplify using the different laws of power and exponents such as negative exponent rule. Also, the factors of the given base in the exponent and then simplify for the resultant value.

Complete step-by-step answer:
Take the given expression –
 $ 2{x^{ - \dfrac{1}{2}}} $
We can observe that the above expression is in the form of $ {x^{ - m}} = \dfrac{1}{{{x^m}}} $ and can be simplified by which states that when exponent is negative, it is expressed as the term in the denominator and exponent power becomes positive. Simply, when the exponent changes its position from numerator to denominator, sign of the power also changes. Positive term changes to negative and vice-versa.
 $ 2{x^{ - \dfrac{1}{2}}} = \dfrac{2}{{{x^{\dfrac{1}{2}}}}} $
The above expression can be re-written as –
 $ 2{x^{ - \dfrac{1}{2}}} = \dfrac{2}{{\sqrt x }} $
This is the required solution.
So, the correct answer is “ $ \dfrac{2}{{\sqrt x }} $ ”.

Note: Always remember that the sign of the power of the exponent changes when it is moved from the numerator to the denominator and vice-versa. Positive power changes to negative and vice-versa. Be careful about the sign convention.