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Question
Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`
Solution
We need to prove that
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`
LHS =
= `x^[a(b - c ) - b( a - c )] ÷ x^(bc)/x^(ac)`
= `x^( ab - ac - ab + bc ) ÷ x^( bc - ac )`
= `x^( ab - ac - ab + bc - bc + ac )`
= `x^0`
= 1
= RHS
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