Question

Simplify by using radical. Rationalize denominators.

`2a^(-1/2)`

Answer 1

`2a^{- (1)/(2) }= \cfrac{2}{a^{ (1)/(2) }} = \cfrac{2}{ √(a) } = \cfrac{2 √(a) }{a}`

Answer 2

`(2\sqrt a)/(a)`

Explanation:

The given equation is
`2a^(-1/2)`

The exponent rule:
`x^(-a)=(1)/(x^a)`

Using this rule, we get

`2a^(-1/2)\\\\=(2)/(a^1/2)`

We can rewrite this in radical form as

`(2)/(\sqrt a)`

Rationalize the denominator by multiplying numerator and denominator by
`\sqrt a`

`(2)/(\sqrt a)\cdot (\sqrt a)/(\sqrt a)`

On simplifying

`(2\sqrt a)/(a)`