How do you simplify #13^4 / sqrt(13^10)#?

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Answer 1 · 2016-06-13T04:36:35

#13^4/(sqrt(13^10))=1/13#

#13^4/(sqrt(13^10)#

= #13^4/(13^10)^(1/2)#

= #13^4/(13^((10xx1/2)))#

= #13^4/13^5#

= #(13xx13xx13xx13)/(13xx13xx13xx13xx13)#

= #1/13#

Answer 2 · 2016-06-14T11:22:14

Demonstration of a very slightly different method.

#1/13#

Another way of writing #sqrt(13^10)" "# is #" "13^(10/2)#

But we have #1/sqrt(13^10)" "# which is the same as #13^(-10/2)#

So #" "13^4/sqrt(13^10) = 13^4xx10^(-10/2)#

But #10/2=5# giving

#13^4xx13^(-5)#

#13^(4-5)= 13^(-1) = 1/13#