Advertisements
Advertisements
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 )`
Advertisements
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 )]`
APPEARS IN
RELATED QUESTIONS
Evaluate:
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`
Simplify:
`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`
Simplify :
`( 3x^2 )^(-3) xx ( x^9 )^(2/3)`
Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`
Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/3)`
Simplify:
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
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 )`
Evaluate the following: `(2^3)^2`
Evaluate the following: `(3^2)^2`
