Question #b143b

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Answer 1 · 2017-10-03T11:11:54

#1/5^(n+7)#

In order to simplify exponents, make sure that the bases are all the same. Change numbers to the product of their prime factors.

#(color(red)(25)^(2n-4))/(5^(3n+1) xx 5^(2n-3) xx 5) = (color(red)((5^2))^(2n-4))/(5^(3n+1) xx 5^(2n-3) xx 5)#

#=(color(red)(5)^(4n-8))/(5^(3n+1) xx 5^(2n-3) xx 5^1)#

Add the indices of like bases when multiplying

#(5^(4n-8))/(5^(5n-1)#

Method 1

Subtract the indices when dividing

#= 1/5^(5n-4n -1-(-8))#

#=1/5^(n+7)#

Method 2

#x^m = 1/(x^-m)#

#(5^(4n-8))/(5^(5n-1)#

#=1/(5^(5n-1) xx 5^(-4n+8))#

#=1/5^(n+7)#

Give the answer without negative or zero indices.