How do you simplify #64^(3/4)times81^(2/3)#?

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Answer 1 · 2017-05-23T19:49:30

#144*2^(1/2)*3^(2/3)#

Step 1. Find the factors of 64 and 81
#64=2^6#
#81=3^4#

#64^(3/4)xx81^(2/3)=(2^6)^(3/4)xx(3^4)^(2/3)#

Step 2. Rewrite the base numbers with powers that will reduce with the fractional exponents

#(2^2*2^4)^(3/4)xx(3^1*3^3)^(2/3)#

Step 3. Multiply the fractional powers through

#(2^(3/2)*2^3)xx(3^(2/3)*3^2)#

#((2*2^2)^(1/2)*2^3)xx(3^(2/3)*3^2)#

#(2^(1/2)*2*2^3)xx(3^(2/3)*3^2)#

#144*2^(1/2)*3^(2/3)#