Question 176744
If we divide 10 by 10 or x by x, or 100 by 100, or any expression by itself, the result will always be 1 (anything divided by itself equals 1).


Based on the Law of Exponents, when dividing expressions with the same base, we need to subtract the exponent in the denominator from the exponent in the numerator. 


All expressions without any exponents actually have an exponent of 1. For example, 10 is actually {{{10^1}}}, x is {{{x^1}}}, 100 is {{{100^1}}}, and so on. When we divide any of these expressions, such as {{{10^1}}}  by itself, we’re supposed to get a result of 1, just like when we divide {{{10^3}}} by itself. This is because anything divided by itself equals 1 (see above). Furthermore, based on the Law of Exponents, and as stated above, {{{10^3}}}  divided by {{{10^3}}} equals {{{10^(3-3)}}}  which equals {{{10^0}}}. Did we not say before that {{{10^3}}}  ÷ {{{10^3}}}, or anything divided by itself equals 1? Therefore, it follows that:

{{{10^3}}}   ÷   {{{10^3}}}     =    1. Also, {{{10^3}}}    ÷   {{{10^3}}}    =   {{{10^(3-3)}}}  which equals {{{10^0}}}.
This means that {{{10^3}}}  ÷ {{{10^3}}}  =   {{{10^(3-3)}}}    =   {{{10^0}}}    =   1.

I hope you now understand why any expression to the power of 0 (zero) always equals 1.