How do you evaluate and simplify #(64^(5/9)*64^(2/9))/4^(3/4)#?

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Answer 1 · 2018-05-09T20:37:10

the answer
#4^(84/36-27/36)=4^(57/36)=4^(19/12)#

#=8.9797#

show below

#(64^(5/9)*64^(2/9))/4^(3/4)#

#(64)^(5/9+2/9)/4^(3/4)=(64)^(7/9)/4^(3/4)#

#64=4^3#

#(4^3)^(7/9)/4^(3/4)=4^(21/9)/4^(3/4)#

#4^(21/9)*4^(-3/4)=4^(21/9-3/4)#

#4^(84/36-27/36)=4^(57/36)=4^(19/12)#

#=4^(19/12)=8.9797#

The index answer is probably better.

Answer 2 · 2018-05-09T21:07:05

#2^(19/6)#

Here are some laws of indices
#x^a xx x ^b=x ^(a+b)#

#x^a -: x^b=x^(a-b)#

#(x^a)^b =x^(a xx b)#

Using the first law
#64^(5/9) xx 64^(2/9)=64^(7/9)#

using the third law
#64=2^6# so #64^(7/9)=(2^6)^(7/9)=>2^(42/9)=2^(14/3)#

#4^(3/4)=(2^2)^(3/4)=>2^(6/4)=2^(3/2)#

Putting these two together

#=> (64^(5/9) xx 64^(2/9))/4^(3/4)=(2^(14/3))/(2^(3/2))#

Using the second law
#(2^(14/3))/(2^(3/2))=2^(14/3-3/2)=2^(28/6-9/6)=2^(19/6)#