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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^0`

= 1

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 10.1 | Page 98
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