To represent $8^6$, you would expand it as follows:

$8^6 = 8 \times 8 \times 8 \times 8 \times 8 \times 8$

To calculate the exact value:

1. Start by computing $8^2$: $8^2 = 64$

2. Then, compute $8^3 = 8^2 \times 8$: $8^3 = 64 \times 8 = 512$

3. Continue with $8^4 = 8^3 \times 8$: $8^4 = 512 \times 8 = 4096$

4. Next, $8^5 = 8^4 \times 8$: $8^5 = 4096 \times 8 = 32768$

5. Finally, $8^6 = 8^5 \times 8$: $8^6 = 32768 \times 8 = 262144$

So, the representation and value of $8^6$ is:

$8^6 = 262144$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How would you represent $8^7$ and calculate its value?
2. What is the significance of exponents in representing large numbers?
3. How does $2^6$ compare with $8^6$ in value?
4. Can you represent $8^6$ using logarithms?
5. How does changing the base affect the result in exponential expressions?

Tip: When calculating large exponents, breaking down the steps can simplify the multiplication process significantly.