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If a and B Are Different Positive Primes Such that `((A^-1b^2)/(A^2b^-4))^7div((A^3b^-5)/(A^-2b^3))=A^Xb^Y,` Find X and Y. - Mathematics

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Question

If a and b are different positive primes such that

`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.

Solution

`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y`

`rArr((a^-7b^14)/(a^14b^-28))div((a^3b^-5)/(a^-2b^3))=a^xb^y`

`rArr(a^(-7-14)b^(14+28))div(a^(3+2)b^(-5-3))=a^xb^y`

`rArr(a^-21b^42)div(a^5b^-8)=a^xb^y`

`rArra^(-21-5)b^(42+8)=a^xb^y`

`rArra^-26b^50=a^xb^y`

⇒ x = -26 and y = 50

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 (2018 (Latest))
Chapter 2: Exponents of Real Numbers
Ex. 2.2 | Q: 18.1 | Page no. 26
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If a and B Are Different Positive Primes Such that `((A^-1b^2)/(A^2b^-4))^7div((A^3b^-5)/(A^-2b^3))=A^Xb^Y,` Find X and Y. Concept: Laws of Exponents for Real Numbers.
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