To simplify the expression 27^8 ÷ 3^2, we can use the properties of exponents.

First, let's simplify 27^8. Since 27 is equal to 3^3, we can rewrite the expression as (3^3)^8.

Using the property (a^m)^n = a^(m*n), we can simplify (3^3)^8 to 3^(3*8) = 3^24.

Now, let's simplify 3^2. 3^2 is equal to 9.

Finally, we can divide 3^24 by 9: 3^24 ÷ 9 = 3^(24-2) = 3^22.

Therefore, 27^8 ÷ 3^2 simplifies to 3^22.