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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 )`
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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 :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`
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)`
If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a x 2-b x 5-c.
Simplify:
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
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`
