Evaluate 5^(−2) (64/125)^(−1/3) without using a calculator?

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#5^(−2) (64/125)^(−1/3)#

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Answer 1 · 2017-07-23T13:26:03

Answer #1/20#

#64 = 4^3. 125 = 5^3#.
So #(64/125)^(-1/3) = (125/64)^(1/3) = 5/4#.
#5/4 * 5^(-2) = 5/4/(5*5) = 1/20#