How do you evaluate the expression #(1/5)^-4/((1/5)^-2(1/5)^-5)# using the properties?

1 Answer
May 25, 2017

Answer:

#1/125#

Explanation:

Set #x=1/5# to make things clearer

#x^(-4)/(x^(-2)x^(-5))#

#=x^(-4)/x^(-7)#

Note that #1/x^(-7)# is the same as #x^7#

Note that #x^(-4)# is the same as #1/x^4#

Putting it all together we have:

#x^7/x^4#
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Method 1: #->x^(7-4)=x^3#

Method 2: #->1/(cancel(x^4))xx cancel(x^4)xxx^3" "=" "x^3#

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Finally, replace #x# with #1/5# and simplify.

#x^3 = (1/5)^3 = 1^3/5^3 = 1/125#

Final Answer