prove that x^a(b-c)/x^b(a-c)÷(x^b/x^a)^c=1
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
8. Prove that { x^[a(b-c)] / x^[b(a-c)] } / { [ x^b / x^a ]^c } = 1
⇒ LHS = { x^[a(b-c)] / x^[b(a-c)] } / { [ x^b / x^a ]^c }
= [ x^(ab-ac) / x^(ab-bc) ] / { [x^b / x^a]^c }
-------------- [ using identity p^m/p^n = p^(m-n) ]
= { x^[(ab-ac)-(ab-bc)] } / { [x^(b-a)]^c }
-------------- [ using identity (p^m)^n = p^(mn) ]
= { x^[ab-ac-ab+bc] } / { x^[c(b-a)] }
= { x^[bc-ac] } / { [x^(bc-ac)] }
-------------- [ using identity p^m/p^n = p^(m-n) ]
= { x^[(bc-ac)-(bc-ac)] }
= { x^[bc-ac-bc+ac] }
= { x^0 } -------------[ using identity p^0 = 1 ]
= 1
LHS = RHS
∴ { [x^a(b-c)] / [x^b(a-c)] } ÷ { (x^b/x^a)^c } =1