can someone help me!? How do I solve this? Algebra 2 ? medal and fan?

Question

anonymous · Answer

probably

ams98 · Answer

Simplify the given expression to radical form, justify each step by identifying the properties of rational exponents used. All work must be shown.$$x \frac{ 2 }{ 3}/ x \frac{ 4 }{ 9}$$

ams98 · Answer

@DebbieG  can you explain this too me?

debbieg · Answer

I don't see any exponents there.  is it:

$\large \dfrac{x^{2/3}}{x^{4/9}}$ ??

ams98 · Answer

yes i wasn't sure how to do that !

debbieg · Answer

Ok, use the rule that:

$\large \dfrac{x^{a}}{x^{b}}=x^{a-b}$

ams98 · Answer

i may be totally wrong but i got $$x ^{2/9}$$

debbieg · Answer

Yes, that's correct.

Now you are supposed to put it into radical form.  Remember, in a rational exponent, the numerator is the power, the denominator is the root.

ams98 · Answer

So: $$\sqrt[9]{x^{2}}$$

debbieg · Answer

$$\Large x^{a/b}=\sqrt[b]{x^a}=\sqrt[b]{x}^a$$

(It doesn't matter is the power goes inside, or outside, the radical... )

Yes, that's it!

ams98 · Answer

okay thank you so much!!

debbieg · Answer

you're welcome. :)