# Thread: Question on Laws of Exponents

1. ## Question on Laws of Exponents

Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

eg: $\displaystyle (x+y)^{1/2} = x^{1/2}+y^{1/2}$

I know if it were $\displaystyle (xy)^{1/2}$ this would be equal to $\displaystyle x^{1/2}y^{1/2}$ but the addition sign is throwing me off.

I've looked at my rules and can't find anything like $\displaystyle (x+y)^2$ laws just the power of the product.

I hope I'm making sense :P

Thanks

2. It's not true. You can check using the Binomial Series...

3. Originally Posted by Substince
Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

eg: $\displaystyle (x+y)^{1/2} = x^{1/2}+y^{1/2}$

I know if it were $\displaystyle (xy)^{1/2}$ this would be equal to $\displaystyle x^{1/2}y^{1/2}$ but the addition sign is throwing me off.

I've looked at my rules and can't find anything like $\displaystyle (x+y)^2$ laws just the power of the product.

I hope I'm making sense :P

Thanks
1. Re-write the expression as:

$\displaystyle \sqrt{x+y}=\sqrt{x} + \sqrt{y}$

2. Square both sides and you'll see that this equation is only true if x = 0 or y = 0

4. wonderful thank you guys!