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Show That: `(X^(A-b))^(A+B)(X^(B-c))^(B+C)(X^(C-a))^(C+A)=1` - Mathematics

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Question

Show that:

`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`

Solution

`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`

LHS = `(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)`

`=[x^((a-b)(a+b))][x^((b-c)(b+c))][x^((c-a)(c+a))]`

`=x^((a^2-b^2))x^((b^2-c^2))x^((c^2-a^2))`

`=x^(a^2-b^2+b^2-c^2+c^2-a^2)`

`=x^0`

= 1

= RHS

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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: 4.5 | Page no. 25
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Show That: `(X^(A-b))^(A+B)(X^(B-c))^(B+C)(X^(C-a))^(C+A)=1` Concept: Laws of Exponents for Real Numbers.
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