Simplifying Fractional Exponents and Can You Explain WHY

Question

How do you solve questions like $2^{1/2}$ and can you explain how this works?

Answer 1

It is known that

x^a × x^b = x^(a+b)

From that, try to input a = b = 0.5 , we get

(x^0.5)×(x^0.5)=x^(0.5+0.5)=x^1=x

(x^0.5)^2=x

By taking the square root of both sides, we obtain

x^0.5= \sqrt{x}

Note that we only take the positive value for the answer.

Answer 2

Let say you have the general problem of $x^{a\over b}$ you can always rewrite this as ${(\sqrt[b] x)^a}$. Just to be clear the b is the bth root not multiplication.