Simplify the Expression: Evaluating 3^6/8^6 Step-by-Step

To solve this problem, we will apply the rule of exponentiation for fractions. This rule states that $\frac{a^n}{b^n} = \left(\frac{a}{b}\right)^n$, where $a$ and $b$ are non-zero numbers and $n$ is an integer.

Let's go through the solution step-by-step:

• Step 1: Recognize that the expression we need to rewrite is $\frac{3^6}{8^6}$.
• Step 2: Apply the power of a fraction rule. According to this rule, $\frac{3^6}{8^6} = \left(\frac{3}{8}\right)^6$.
• Step 3: Thus, the expression $\frac{3^6}{8^6}$ simplifies to $\left(\frac{3}{8}\right)^6$.

The solution to the problem is that the expression can be rewritten as $\left(\frac{3}{8}\right)^6$.