#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#