Simplify by using radical. Rationalize denominators. 2a^{(-1)/(-2) }

Question

Simplify by using radical. Rationalize denominators.


`2a^{(-1)/(-2) }`

Answer 1

Explanation:

First of all,
`(-1)/(-2)` is equal to
`(1)/(2)` because a negative divided by a negative is positive. So now we've got
`2a^(1)/(2)`. Well, a fractional exponent, when simplified, is a root. For example,
`x^(1)/(3)` is equal to
`\sqrt[3]{x}`, and
`x^(2)/(5)` is equal to
`\sqrt[5]{x^2}`.

Now this is where people make mistakes. Remember,
`2a^(1)/(2)` is really
`2*a^(1)/(2)`, which means only a is raised to the exponent. We would only raise 2a to the power of
`(1)/(2)` if our term was
`(2a)^(1)/(2)`. But since our term is
`2*a^(1)/(2)` we raise a to the power of
`(1)/(2)` which is the same as
`\sqrt[2]{a}` or just
`√(a)`. Then we multiply that result by 2 and we have
`2√(a)` which is fully simplified.