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.!