The problem is to simplify the given expressions using the properties of exponents. The general form is $a^m \cdot a^n$, which simplifies to $a^{m+n}$. We have to apply this rule to each of the ten given expressions.

1. Problem Description

The problem is to simplify the given expressions using the properties of exponents. The general form is $a^m \cdot a^n$, which simplifies to $a^{m+n}$. We have to apply this rule to each of the ten given expressions.

2. Solution Steps

1. $7^4 \cdot 7^7 = 7^{4+7} = 7^{11}$

2. $9^6 \cdot 9^8 = 9^{6+8} = 9^{14}$

3. $2^7 \cdot 2^4 = 2^{7+4} = 2^{11}$

4. $5^6 \cdot 5^8 = 5^{6+8} = 5^{14}$

5. $7^9 \cdot 7^3 = 7^{9+3} = 7^{12}$

6. $4^7 \cdot 4^2 = 4^{7+2} = 4^9$

7. $5^8 \cdot 5^7 = 5^{8+7} = 5^{15}$

8. $4^2 \cdot 4^5 = 4^{2+5} = 4^7$

9. $9^8 \cdot 9^3 = 9^{8+3} = 9^{11}$

1

0. $5^8 \cdot 5^6 = 5^{8+6} = 5^{14}$

3. Final Answer

1. $7^{11}$

2. $9^{14}$

3. $2^{11}$

4. $5^{14}$

5. $7^{12}$

6. $4^9$

7. $5^{15}$

8. $4^7$

9. $9^{11}$

1

0. $5^{14}$