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^0`
= 1
RELATED QUESTIONS
Evaluate:
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
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 a positive index:
`(32)^(-2/5) ÷ (125)^(-2/3)`
If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a x 2-b x 5-c.
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 )`
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: `(3^2)^2`
Find the value of 46 × 4−4.
