The problem is to simplify the given expressions involving exponents and quotients. We will address each expression one by one.

1. Problem Description

The problem is to simplify the given expressions involving exponents and quotients. We will address each expression one by one.

2. Solution Steps

Problem 2: $8^{24}$

This expression is already simplified, assuming we don't want to calculate the very large number.

Problem 4: $\frac{8^4}{8^3}$

Using the quotient rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{8^4}{8^3} = 8^{4-3} = 8^1 = 8$

Problem 6: $\frac{8^2}{8^2}$

Using the quotient rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{8^2}{8^2} = 8^{2-2} = 8^0 = 1$

Problem 8: $8^{69}$

This expression is already simplified, assuming we don't want to calculate the very large number. However, the image suggests to raise the power to another power; I'll proceed assuming the problem is $8^{6^9}$ and apply the power of a power rule. According to this rule, $(a^m)^n=a^{m*n}$. But since the original expression is $8^{69}$, it's best to write down this simplified version.

Problem 10: $\frac{7^7}{7^9}$

Using the quotient rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{7^7}{7^9} = 7^{7-9} = 7^{-2} = \frac{1}{7^2} = \frac{1}{49}$

3. Final Answer

2. $8^{24}$

3. $8$

4. $1$

5. $8^{69}$

6. $\frac{1}{49}$