$$3^5 + {1\over3^5}=?$$
My first instinct was to rewrite the second term as $3^{-5}$. Since the base is $3$, rewrite as $3^{5+-5}$. It simplifies to $3^0= 1$. Apparently this is incorrect. Can anyone please explain why?
[Math] Adding fractions with exponents
fractions
Best Answer
This is incorrect because the exponent rule that you were thinking of is: $$a^b\cdot a^c = a^{b + c}$$ So if you had $3^{5}\cdot 3^{-5}$ then you could use that rule: $$3^{5}\cdot 3^{-5} = 3^{0}$$.