How would I simplify $\displaystyle (144a^8b^2)^1/2$
I didn't know how to make the 1 over 2 smaller so I tried my bestbut its suppose to be in the top right, thanks if you can help
It means square root,Originally Posted by Ronis
$\displaystyle \sqrt{144a^8b^2}=\sqrt{144}\cdot \sqrt{a^8}\cdot \sqrt{b^2}=12a^4b$
-----
Note: (this is not for you) I know that $\displaystyle \sqrt{b^2}\not = b$, so do not bother me with that. Because in schools terms are positive.
Hello, Ronis!
You have to enclose the entire exponent in braces
. like this: (144a^8b^2)^{1/2}
You can even write: (144^8b^2)^{\frac{1}{2}}
How would I simplify $\displaystyle (144a^8b^2)^{\frac{1}{2}}$
Each factor is raised to the ½ power: .$\displaystyle (144)^{\frac{1}{2}}(a^8)^\frac{1}{2}}(b^2)^{\frac{ 1}{2}}$
Since $\displaystyle 144 = 12^2$, we have: .$\displaystyle (12^2)^{\frac{1}{2}}(a^8)^{\frac{1}{2}}(b^2)^{ \frac{1}{2}} $
Use that third property of exponents: .$\displaystyle 12^{(2\cdot\frac{1}{2})} \cdot a^{(8\cdot\frac{1}{2})}\cdot b^{(2\cdot\frac{1}{2})} $
. . And we get: .$\displaystyle 12^1\cdot a^4\cdot b^1\;=\;12a^4b$
Just for reference...
$\displaystyle \sqrt[2]{x}=x^{\frac{1}{2}$
also,
$\displaystyle \sqrt[3]{x}=x^{\frac{1}{3}$
you can remember the rule,
$\displaystyle \sqrt[a]{x}=x^{\frac{1}{a}$
also the rules of powers:
$\displaystyle x^a\times x^b=x^{(a+b)}$
$\displaystyle (x^a)^b=x^{(a\times b)}$
$\displaystyle x^{-a}=\frac{1}{x^a}$