What does the quotient rule of exponents say?

See explanation Explanation: The quotient rule of exponents is:#(a^m)/(a^n)=a^(m-n); a!=0#What this means that if you are dealing with a quotient problem involving exponents, then you can subtract the exponents if the bases are the same.This is how it works. Lets consider the following:#(a^7)/(a^3)#If we write out the exponents like so...#(a^7)/(a^3)=(a*a*a*a*a*a*a)/(a*a*a)# ... we can cancel out some of the #a#'s because #a/a=1##:. a^7/a^3=(a*a*a*a*color(red)cancel(a)*color(red)cancela*color(red)cancela)/(color(red)cancela*color(red)cancela*color(red)cancela)=(a*a*a*a)/1=a^4#This is essentially subtraction and rather then writing out every term we can subtract the exponents like so:#a^7/a^3=a^(7-3)=a^4#Remember: You can only apply this rule if the bases are the same!For example we could not simply #a^4/b^2# much further because the bases are not the same so there aren't any like terms to combine.Lets look at a final example:Simplify:#(a^13*b^3*c^5)/(a^5*b^2*c^2)#Here we have three different bases so we can treat this as three small problems if we split up the problem such that:#(a^13*b^3*c^5)/(a^5*b^2*c^2)=color(blue)(a^13/a^5)*color(red)(b^3/b^2)*color(green)(c^5/c^2)#We now apply the rule:#color(blue)(a^(13-5))*color(red)(b^(3-2))*color(green)(c^(5-2))= color(blue)(a^(8))*color(red)(b^(1))*color(green)(c^(3))= a^8bc^3#I hope this helped. :)