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!

Learn how to simplify the exponential expression [a^5 ÷ a^3] × a^6 using the laws of exponents. This problem demonstrates division and multiplication rules for exponents and is suitable for students in Grades 6-8.

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