# Simplifying Fractional Exponents and Can You Explain WHY

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

• "$2^{1\over 2}$" isn't a question ... Jan 14, 2020 at 23:09
• What Noah said, but the bigger nitpick here is that expressions can't be solved, only simplified. $2^{1/2}$ can't be simplified any further, but it can be rewritten as $\sqrt 2$. Is there a specific problem you're working on that you need help with? It's unclear what you're asking.
– user307169
Jan 14, 2020 at 23:10
• Thank you, I am in grade 6 and learning algebra Jan 14, 2020 at 23:15

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.

• Thank you so much for answering my question. Jan 14, 2020 at 23:45

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.

• This is a good answer and i kind of understand. Jan 14, 2020 at 23:32
• I am really glad to hear that. Sorry if i didnt manage to make it looks good. Jan 15, 2020 at 10:58