Advertisements
Advertisements
рдкреНрд░рд╢реНрди
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
рдЙрддреНрддрд░
`(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
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Evaluate:
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Evaluate:
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
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 :
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`
If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a x 2-b x 5-c.
If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 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 )`
`[(3/7)^-3]^4` = ______
