How do you simplify ${(10)^{ - 2}} - {( - 10)^{ - 2}}$?

Hint: According to the question we have to determine the value of ${(10)^{ - 2}} - {( - 10)^{ - 2}}$. So, first of all to determine the value of ${(10)^{ - 2}} - {( - 10)^{ - 2}}$ we have to use the formula to find the inverse or the negative power which is as explained below:

Formula used: $ \Rightarrow {a^{ - n}} = \dfrac{1}{{{a^n}}}............(A)$
Now, we have to find the square of the term having square and as we know that when a term having a negative sign is multiplied with the term having negative sign then it will become positive and if a positive term is multiplied with the negative term then it will become negative.
Now, we have to add or subtract the terms which can be added or subtracted or we can say that we have to add or subtract the variables with the same variable and constant terms with the constant terms.

Complete step-by-step solution:
Step 1: First of all to determine the value of ${(10)^{ - 2}} - {( - 10)^{ - 2}}$ we have to use the formula (A) to find the inverse or the negative power which is as explained in the solution hint. Hence,
$ = \dfrac{1}{{{{(10)}^2}}} - {\left( { - \dfrac{1}{{10}}} \right)^2}$
Step 2: Now, we have to find the square of the term having square and as we know that when a term having a negative sign is multiplied with the term having negative sign then it will become positive and if a positive term is multiplied with the negative term then it will become negative. Hence,
$ = \dfrac{1}{{100}} - \dfrac{1}{{100}}$
Step 3: Now, we have to add or subtract the terms which can be added or subtracted or we can say that we have to add or subtract the variables with the same variable and constant terms with the constant terms. Hence,
$ \Rightarrow \dfrac{1}{{100}} - \dfrac{1}{{100}} = 0$

Hence, with the help of the formula (A) we have determined the solution of the given expression ${(10)^{ - 2}} - {( - 10)^{ - 2}}$ which is 0.

Note: When a negative term or a number is multiplied with an-other negative term or number then it will become negative and if a positive term is multiplied with a negative term it will become negative.
On finding the square of the term having negative sign it will become positive because multiplying two negative signs will become positive.