Let's simplify each of these expressions using exponent rules.

a) $4^8 \times 4^3$

Using the rule for multiplying powers with the same base, we add the exponents: $4^8 \times 4^3 = 4^{8+3} = 4^{11}$

b) $6^6 \times 6^2$

Similarly, for powers with the same base, add the exponents: $6^6 \times 6^2 = 6^{6+2} = 6^8$

c) $8^7 \div 8$

Using the rule for dividing powers with the same base, subtract the exponents: $8^7 \div 8^1 = 8^{7-1} = 8^6$

d) $7^8 \div 7^3$

For division, subtract the exponents: $7^8 \div 7^3 = 7^{8-3} = 7^5$

Would you like further details on any of these rules?

Here are 5 related questions:

1. How would you simplify $9^5 \times 9^2$?
2. What is $5^4 \div 5^2$?
3. If you have $10^6 \times 10^3$, how do you simplify it?
4. Simplify $12^8 \div 12^1$.
5. How do the rules for exponents change when adding or subtracting bases?

Tip: Always apply the same rules of addition or subtraction of exponents only when the base remains the same.