Surds and Indices Practice Test 2

Question : 9 of 17

Marks: +1, -0

(x^b/x^c)^{(b+c-a)}.(x^c/x^a)^{(c+a-b)}.(x^a/x^b)^{(a+b-c)}=?

Solution:

(x^b/x^c)^{(b+c-a)}.(x^c/x^a)^{(c+a-b)}.(x^a/x^b)^{(a+b-c)}

=(x^(b-c))^{(b+c-a)}.(x^( c-a))^{(c+a-b)}.(x^(a-b ))^{(a+b-c)}

=x^{(b^2+bc-ab-bc-c^2+ac)}.x^{(c^2+ac-bc-ac-a^2+ab)}.x^{(a^2+ab-ac-ab-b^2+bc)}

=x^{(b^2-ab-c^2+ac+c^2-bc-a^2+ab+a^2-ac-b^2+bc)}

=x^0=1

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