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 )`
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
APPEARS IN
RELATED QUESTIONS
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Evaluate :
`7^0 xx (25)^(-3/2) - 5^(-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)`
Evaluate:
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`
Simplify the following and express with positive index:
`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`
Simplify :
`[ 8^3a xx 2^5 xx 2^(2a) ]/[ 4 xx 2^(11a) xx 2^(-2a) ]`
If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,
Prove that : am - n. bn - l. cl - m = 1
Evaluate the following: `(2^3)^2`
