How do you simplify #((8^(-1/3))^2)#?

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Answer 1 · 2016-05-22T19:38:10

#1/4# #=0.25#

#(8^(-1/3))^2#

we know,
#8^(-1/3) = 1/2# by applying exponent rule i.e #a^-b =1/(a^b# #=1/8^(1/3)# and #8^(1/3) = 2#

So,
#(1/2)^2#

#1/4# = #0.25#

Answer 2 · 2016-05-22T20:35:32

#1/4#

Very slightly different approach!

Write as:# " "8^(-1/3)xx8^(-1/3) = 8^(-2/3) = 1/(root(3)(8^2)) = 1/4#