Let's analyze and solve the expression given in the image, which is:

$\frac{6^{-6}}{6^{-8}} \times 6^4$

Step 1: Simplify the fraction

Using the properties of exponents, specifically the rule $\frac{a^m}{a^n} = a^{m-n}$, we can simplify the first part of the expression:

$\frac{6^{-6}}{6^{-8}} = 6^{-6 - (-8)} = 6^{-6 + 8} = 6^2$

Step 2: Multiply the simplified fraction by $6^4$

Now the expression becomes:

$6^2 \times 6^4$

Using the rule for multiplying exponents with the same base $a^m \times a^n = a^{m+n}$, we can simplify this further:

$6^2 \times 6^4 = 6^{2+4} = 6^6$

Final Answer:

The expression is equivalent to:

$6^6$

Would you like any further clarification or details?

Here are 5 related questions for further practice:

1. What is $\frac{a^3}{a^2} \times a^5$?
2. Simplify the expression $\frac{7^{-3}}{7^{-5}} \times 7^8$.
3. How would you simplify $\frac{5^6}{5^2} \times 5^3$?
4. If $x = 2^4 \times 2^{-2}$, what is the value of $x$?
5. What is the result of $10^{-3} \times 10^5$?

Tip: When simplifying expressions involving exponents, always apply the exponent rules for division and multiplication to reduce complexity efficiently.