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If ((A^-1b^2 )/(A^2b^-4))^7 ÷ (( A^3b^-5)/(A^-2b^3))^-5 = A^X . B^Y , Find X + Y. - Mathematics

Sum

If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.

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Solution

`((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y`

⇒ `((b^6)/( a^3))^7 ÷ ((a^5)/(b^8))^-5 = a^x . b^y`

⇒ `((b^6)/( a^3))^7 ÷ ((b^8)/(a^5))^5 = a^x . b^y`

⇒ `((b^42)/(a^21)) ÷ ((b^40)/(a^25)) = a^x . b^y`

⇒ `((b^42)/(a^21)) xx ((a^25)/(b^40)) = a^x . b^y`

⇒ b2 x a4 = ax x by
⇒ x = 4 and y = 2
⇒ x + y = 4 + 2 = 6

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 4 | Page 101
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