To solve the expression $[a^5 \div a^3] \times a^6$, follow these steps:

1. Apply the division rule of exponents: $\frac{a^m}{a^n} = a^{m-n}$.

$a^5 \div a^3 = a^{5-3} = a^2$

2. Now, multiply the result by $a^6$. Use the multiplication rule of exponents: $a^m \times a^n = a^{m+n}$.

$a^2 \times a^6 = a^{2+6} = a^8$

Thus, the solution is:

$a^8$

Would you like more details or further clarification?

Here are 5 related questions to expand on this topic:

1. How would you simplify $(a^7 \div a^4) \times a^2$?
2. What is the result of $(x^8 \div x^2) \times x^3$?
3. How do the laws of exponents apply to negative exponents, such as $\frac{a^{-3}}{a^{-5}}$?
4. What happens when you divide two exponents with the same base but equal powers, e.g., $b^3 \div b^3$?
5. How do you simplify expressions with fractional exponents, like $\frac{a^{5/2}}{a^{1/2}}$?

Tip: When multiplying or dividing powers with the same base, remember to add or subtract the exponents accordingly!