1. **State the problem:** Simplify the expression $$ (25^{-1}) + (25^{-2}) $$ and understand why the answer might be 26. 2. **Recall the rules for negative exponents:** For any nonzero number $a$ and positive integer $n$, $$ a^{-n} = \frac{1}{a^n} $$ 3. **Apply the rule to each term:** - $$ 25^{-1} = \frac{1}{25} $$ - $$ 25^{-2} = \frac{1}{25^2} = \frac{1}{625} $$ 4. **Rewrite the expression:** $$ (25^{-1}) + (25^{-2}) = \frac{1}{25} + \frac{1}{625} $$ 5. **Find a common denominator:** The common denominator is 625. 6. **Convert fractions:** $$ \frac{1}{25} = \frac{25}{625} $$ 7. **Add the fractions:** $$ \frac{25}{625} + \frac{1}{625} = \frac{26}{625} $$ 8. **Interpretation:** The simplified value is $$ \frac{26}{625} $$ which is approximately 0.0416, not 26. 9. **Why might the answer be 26?** Possibly a misunderstanding: the numerator after adding fractions is 26, but the entire fraction is $$ \frac{26}{625} $$, not 26. **Final answer:** $$ (25^{-1}) + (25^{-2}) = \frac{26}{625} $$