How do you simplify #(125/64)^(-2/3)#?

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Answer 1 · 2015-10-23T05:23:46

#(125/64)^(-2/3) = color(green)(16/25#

A property of exponents states that
#color(blue)((a/b)^-m = (b/a)^m#

Hence #(125/64)^(-2/3) = (64/125)^(2/3)#

# = (64/125)^((1/3)*2)#

We also know that #color(blue)(a^(m*n) = (a^m)^n#

# = {(64/125)^(1/3)}^2#

#color(blue)(a^(1/m) = rootm(a)#

# = (root3(64/125))^2#

# = (root3(4^3/5^3))^2#

# = (root3((4/5)^3))^2#

# = (4/5)^2#

# = 4^2/5^2#

# = color(green)(16/25#