#color(green)("Note that you are 'not allowed' to divide by 0")#
#color(green)("So "x/x=0/0 !=1" It is 'undefined' (not allowed)")#
Consider #4/4 =1# now compare that to #x/x=1#
Considering the same thing but by using powers
#color(brown)("If you have "1/x" you can write this as "x^(-1))#
'.....................................................
Now think about #x xx x = x^2#
But #x# can be written as #x^1#
So #x xx x=x^2 -> x^1xxx^1=x^2#
#color(brown)("So "x^1xxx^1=x^(1+1)=x^2)#
'.............................................................
#color(blue)("Putting it all together")#
So if we have #x/x# this can be written as
#x xx 1/x#
# = x^1xxx^(-1)#
# = x^(1-1)#
# = x^0 = 1#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering your question")#
Thus #m^0=1# so #5m^0= 5xx1 = 5#
