How do you simplify #(100^(1/2))^-4#?

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Answer 1 · 2017-01-03T01:31:48

See full simplification process below

First step is to simplify the terms in the parenthesis:

#(100^(1/2))^-4 = 10^-4#

Next we can use this rule for exponents to further simplify:

#x^color(red)(a) = 1/x^color(red)(-a)#

Substituting gives:

#10^color(red)(-4) = 1/10^color(red)(- -4) = 1/10^4 = 1/(10 xx 10 xx 10 xx 10) =#

#1/10000# or #0.0001#