How do you evaluate and simplify $(12^(3/5)*8^(3/5))^5$ ?

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Answer 1 · 2016-08-31T16:18:03

$884736$ .

The Expression $=(12^(3/5)*8^(3/5))^5$

$=(12^(3/5))^5*(8^(3/5))^5...............["Rule" : (ab)^m=a^m.b^m]$

$=12^((3/5*5))*8^((3/5*5))............["Rule" : (a^m)^n=a^((m*n))]$

$=12^3*8^3$

$=1728*512=884736$ .

Alternatively,

The Expression $=(12^(3/5)*8^(3/5))^5$

$={(12*8)^(3/5)}^5..................["Rule" : a^m*b^m=(ab)^m]$

$=(96)^(3/5*5).......................["Rule" : (a^m)^n=a^((m*n))]$

$=96^3$

$=(100-4)^3$ .

Here, we use, $(x-y)^3=x^3-y^3-3xy(x-y)$ , and get,

$96^3=100^3-4^3-3(100)(4)(100-4)$

$=1000000-64-1200(100-4)$

$=1000000-64-120000+4800$

$=1004800-120064$

$=884736$ , as before!

Enjoy Maths.!

How do you evaluate and simplify (12^(3/5)*8^(3/5))^5(12^(3/5)*8^(3/5))^5?