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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 ) - Mathematics

Sum

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 )`

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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^(( a^3 + b^3 + b^3 + c^3 + c^3 + a^3 ))`

= `x^[2( a^3 + b^3 + c^3 )]`

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 10.2 | Page 98
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