[SOLVED] Simplyfying

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February 1st 2009, 03:25 AM
mj.alawami

[SOLVED] Simplyfying

$\sqrt[4]{x^6}$

Attempt
$x^1\sqrt[4]{x^2}$
OR
$\sqrt[2]{x^3}$

Which of the following is correct and why?
February 1st 2009, 03:47 AM
earboth

Quote:

Originally Posted by mj.alawami

$\sqrt[4]{x^6}$

Attempt
$x^1\sqrt[4]{x^2}$
OR
$\sqrt[2]{x^3}$

Which of the following is correct and why?

Both!

$\sqrt[4]{x^6} = \left(x^6\right)^{\frac14} = x^{\frac64} = x^{1+\frac12} = x \cdot \sqrt{x}$

$\sqrt[4]{x^6} = \left(x^6\right)^{\frac14} = x^{\frac64} = x^{\frac32} = \sqrt{x^3}$

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