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Convert them to exponents and then divide. \[\sqrt[n]{a} = a^{1/n}\]
So for example \[\sqrt[4]{x^3}\text{ divided by }\sqrt[3]{x^2} \] would be \[\frac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\] or \[x^{\frac{3}{4}-\frac{2}{3}}\]
Which would then be \[x^{\frac{1}{12}}=\sqrt[12]{x}\]

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Sometimes the test wants you to give you answer in terms of a radical, then you might have to convert it back. If they will accept the exponent version, then that is the way to go.
yes, what is \[\frac{x^{5/12}}{x^{1/6}}\] Just because they want it in radical form as the answer doesn't mean that you can't do all the work in exponent form and then reconvert. \[\frac{x^a}{x^b}=x^{a-b}\] This seems easier to me than trying to figure out the radical forms.
Um. No. What is \[\frac{5}{12}-\frac{1}{6}\]?
You are forgetting to put them into common denoms. 5\12 - 1\6 = 5\12 -2\12 = 3\12 = 1\4
When you divide same base different exponents you subtract the exponents from one another. \[\frac{aaaaa}{aa}=\frac{a^5}{a^2}\] \[\frac{aaa}{1}\frac{aa}{aa}=aaa = a^3= a^{5-2}=a^3\]
No, x^2/3 is wrong. Sorry. If you want to do it in radical form you can. \[\frac{\sqrt[12]{x^5}}{\sqrt[6]{x}}\] can also be done realizing that \[\sqrt[5]{a} = \sqrt[10]{a^2}\] so you can do it that way. You need to convert the index 6 to a twelve
Sure.
index 12√x^5 x index 6√x doesn't it mean, \(\huge \sqrt[12]{x^5} \times\sqrt[6]x\)
It does say to divide the expressions though. \[\frac{\sqrt[12]{x^5}}{\sqrt[6]{x}}\to\frac{\sqrt[12]{x^5}}{\sqrt[12]{x^2}}\to \] \[\sqrt[12]{\frac{x^5}{x^2}}\to\sqrt[12]{x^{5-2}}\to\sqrt[12]{x^3}\to \sqrt[4]{\sqrt[3]{x^3}}\to\sqrt[4]{x}\]
The main methods you need to know is that 1) \[\sqrt[5]{x} = \sqrt[10]{x^2}\] 2) \[\frac{\sqrt[12]{a}}{\sqrt[12]{b}}=\sqrt[12]{\frac{a}{b}}\] Yes the fourth root of x is the answer in radical form.
The reason why I suggested immediately to use your exponent conversion is that, if this is algII, you probably learned the exponent rules prior to this and can then use them rather than memorize another set of rules for radicals.
for questions like these, you need to be able to write down the 4 or so rules of exponents and the radical methods as well. Good luck and don't give up. exponents give a lot of people confusion.
i hope to question was avtually to divide... its bit unclear....
*actually
yes it was. I am working on the fact that it said to divide the two expressions.
the 'x' in middle is throwing me off...
can u confirm the question abbie ?

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