Calculate

3¹⁰⁰⁰+ 3¹⁰⁰⁰+ 3¹⁰⁰⁰/ 3¹⁰⁰¹+ 3¹⁰⁰⁰+ 3⁹⁹⁹

Step 1. Understanding the problem Try calculating 3¹⁰⁰¹, 3¹⁰⁰⁰or 3⁹⁹⁹on a calculator. What happens? Why? We see that a calculator is not particularly helpful in solving this problem.

Step 2. Looking for a good idea We need to calculate the value of a fraction, but we are unable to evaluate the individual terms in the numerator and in the denominator of this fraction. On the other hand, these individual terms in the numerator and in the denominator of the fraction look very similar: all are powers of 3. What ways of simplifying a complex fraction do you know? Could any of these be used to simplify the fraction before us?

Step 3. Implementing the idea Try to factor both the numerator and the denominator of this fraction. Then reduce it to lowest terms. Now, solve