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Simplify: `(X^(A+B)/X^C)^(A-b)(X^(B+C)/X^A)^(B-c)(X^(C+A)/X^B)^(C-a)` - Mathematics

Simplify:

`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`

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Solution

`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`

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

`=(x^(a^2-b^2)/x^(ca-bc))(x^(b^2-c^2)/x^(ab-ac))(x^(c^2-a^2)/x^(bc-ab))`

`=x^(a^2-b^2+b^2-c^2+c^2-a^2)/x^(ca-bc+ab-ac+bc-ab)`

`=x^0/x^0`

= 1

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Exercise 2.2 | Q 21.1 | Page 27
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