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Question
Simplify:
`( x^a/x^-b )^( a^2 - ab + b^2 ) xx ( x^b/x^-c )^( b^2 - bc + c^2 ) xx ( x^c/x^-a )^( c^2 - ca + a^2 )`
Solution
`( x^a/x^-b )^( a^2 - ab + b^2 ) xx ( x^b/x^-c )^( b^2 - bc + c^2 ) xx ( x^c/x^-a )^( c^2 - ca + a^2 )`
= `( x)^(( a + b )( a^2 - ab + b^2)) xx ( x)^((b + c)(b^2 - bc + c^2)) xx ( x)^((c + a)(c^2 - ca + a^2))`
= `x^( a^3 + b^3 ) xx x^(b^3 + c^3 ) xx x^(c^3 + a^3)`
= `x^( a^3 + b^3 + b^3 + c^3 + c^3 + a^3 )`
= `x^(( 2a^3 + 2b^3 + 2c^3))`
= `x^[2( a^3 + b^3 + c^3 )]`
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