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प्रश्न
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 )`
उत्तर
`( 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^0`
= 1
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