Consider the example of #a^2#, this is #a^1xxa^1=a^2=a^(1+1)#
So #a^5#, if so chosen, could be written as #a^(2+3)=a^2xxa^3#
#color(blue)("Back to your question")#
#color(brown)("Method 1")#
Write #15^4" as "15^4 xx1#
Write #15^6" as "15^(4+2) = 15^4xx15^2#
So #15^4/15^6=(15^4xx1)/(15^4xx15^2)#
This is the same as #15^4/15^4xx1/15^2#
But #15^4/15^4=1# giving
#color(brown)(15^4/15^6=1/15^2 = 1/225)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Method 2")#
Consider the example:# 1/a^2 = a^(-2)#
Write #15^4/15^6" as "15^4xx15^(-6)#
#color(brown)(=15^(4-6)=15^(-2) = 1/15^2 =1/225)#
