(8a^8)^.5

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- Mar 31st 2010, 03:41 PMPrincessIsraelsimple question but forgot how to solve
(8a^8)^.5

- Mar 31st 2010, 03:44 PMpickslides
You can't sovle it unless it has an equals sign.

- Mar 31st 2010, 03:48 PMStroodle
I think you mean simplify, not solve?

$\displaystyle (8a^8)^{\frac{1}{2}}$

$\displaystyle =(2^3a^8)^{\frac{1}{2}}$

$\displaystyle =2^{\frac{3}{2}}a^{\frac{8}{2}}$

$\displaystyle =2^{\frac{3}{2}}a^4$

$\displaystyle =2\sqrt{2}a^4$ - Mar 31st 2010, 03:48 PMPrincessIsrael
haha okay so what does it equal

- Mar 31st 2010, 03:48 PMJhevon
Did you mean simplify?

A nice way to do this: factor the radicand (do you know what that is?) using the largest factors you can find the square root of. then break the problem into two sqaure roots. In the first, throw everything that simplifies, in the last, everything that doesn't

$\displaystyle \sqrt{8a^8} = \sqrt{4 \cdot 2 \cdot a^8}$

$\displaystyle = \sqrt{4a^8} \cdot \sqrt 2$

$\displaystyle = 2a^4 \sqrt 2$ - Apr 1st 2010, 01:54 AMHallsofIvy