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Would someone mind helping me by checking my answer that I have worked out? I think I am correct... but I can't seem to find an answer for it anywhere so I want to be sure I am right. Thank you in advance!

$$ (x^4 y)^{2/3} (xy^3)^{1/3} \over x^{2/3} y^{2/3} $$

The question asked me to simplify and ensure only positive exponents are remaining.

$$ (x^{8/3} y^{2/3})(x^{1/3} y^{3/3}) \over x^{2/3} y^{2/3} $$

$$x^{9/3} y^{5/3} \over x^{2/3} y^{2/3} $$

$$x^{7/3} y^{3/3}$$

Final answer:

$$ x^{7/3} y $$

Dani
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2 Answers2

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Your answer is entirely correct. Well done. And because all exponents ended up in the "numerator" they are positive.

BeaumontTaz
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Yes! It is correct! If you want to check an identity one idea is to to set the variables some scalars. Sometimes it is very helpful.

Another idea which is helpful here is to get rid of denumerator like this: $$ \frac{(x^4y)^{2/3} (xy^3)^{1/3}}{x^{2/3}y^{2/3}} = {(x^4y)^{2/3} (xy^3)^{1/3}}{x^{-2/3}y^{-2/3}} = x^{8/3}y^{2/3}x^{1/3}y x^{-2/3}y^{-2/3} = x^{8/3+1/3-2/3}y^{2/3+1-2/3} = x^{7/3}y. $$

Mohammad Khosravi
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