Question

Help super confused

Answer 1

9514 1404 393

Answer:

`7x^2\sqrt[3]{x^2}`

Explanation:

Apparently, you're trying to remove the radical from the denominator.

Here, that is done by multiplying by a factor that makes the denominator a perfect cube. In order to keep from changing the value of the expression, the numerator needs to be multiplied by the same factor.

The problem now is to make sense of this mish-mash of radicals and exponents.

`=\frac{7x^4\sqrt[3]{x^8}}{(\sqrt[3]{x^4})^3}=\frac{7x^4\sqrt[3]{x^6\cdot x^2}}{x^4}=\boxed{7x^2\sqrt[3]{x^2}}`

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I think I would come at this a little differently.

`\frac{7x^4}{\sqrt[3]{x^4}}=7x^{4-(4)/(3)}=7x^{2(2)/(3)}=7x^2\sqrt[3]{x^2}`

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This makes use of the rules of exponents and radicals ...

∛a = a^(1/3)

(a^b)^c = a^(bc)

(a^b)/(a^c) = a^(b-c)