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If a and B Are Distinct Primes Such that `Root3 (A^6b^-4)=A^Xb^(2y),` Find X and Y. - Mathematics

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ConceptLaws of Exponents for Real Numbers

Question

If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.

Solution

Given `root3 (a^6b^-4)=a^xb^(2y)`

`rArr(a^6b^-4)^(1/3)=a^xb^(2y)`

`rArra^(6xx1/3)b^(-4xx1/3)=a^xb^(2y)`

`rArra^2b^(-4/3)=a^xb^(2y)`

⇒ x = 2 and y = -2/3

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Solution If a and B Are Distinct Primes Such that `Root3 (A^6b^-4)=A^Xb^(2y),` Find X and Y. Concept: Laws of Exponents for Real Numbers.
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