How do you simplify #(10^(3/4)*4^(3/4))^(-4)#?

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Answer 1 · 2016-12-06T21:17:47

#1/64000#

Following the rules for exponents this problem can be rewritten as:

First #color(red)(X^n*Y^n = XY^n)#; we can apply this to the terms within parenthesis:

#(10^(3/4)*4^(3/4))^-4 -> ((4*10)^(3/4))^-4 -> (40^(3/4))^-4#

Next #color(red)((X^n)^m = X^(n*m))# can be apply to our simplification:

#(40^(3/4))^-4 -> 40^((3/4)*-4) -> 40^-3#

Finally, #color(red)(X^-n = 1/X^n)# can applied to give:

#40^-3 -> 1/40^3 -> 1/(40*40*40) -> 1/64000#