To solve this question:

We are tasked with simplifying $6^5 \cdot 6^5$.

Step 1: Apply the rule of exponents

When multiplying exponential terms with the same base, you add their exponents: $a^m \cdot a^n = a^{m+n}$ Here, the base $a$ is $6$, and the exponents are both $5$. So, $6^5 \cdot 6^5 = 6^{5+5} = 6^{10}.$

Final Answer:

The equivalent expression is $6^{10}$.

Would you like further clarification or have additional questions? Here are five related questions for you to explore:

1. What is the rule for dividing exponents with the same base?
2. How would you simplify $6^3 \cdot 6^2$?
3. What happens when you raise an exponent to another power, such as $(6^5)^2$?
4. What is $6^{10}$ written out as a standard number?
5. Can the rule of exponents apply if the bases are different?

Tip: Always check the base before applying exponent rules—these rules only work if the bases are the same.