Simplify Complex Expression: [a⁴/a³ × a⁸/a⁷] ÷ a¹⁰/a⁸

To solve this problem, we need to simplify the given expression using the rules of exponents:

First, simplify inside the brackets:
$\frac{a^4}{a^3} \times \frac{a^8}{a^7} = a^{4-3} \times a^{8-7} = a^1 \times a^1 = a^{1+1} = a^2$

Now, handle the entire expression, dividing it by $\frac{a^{10}}{a^8}$:
$\frac{a^2}{\frac{a^{10}}{a^8}} = a^2 \times \frac{a^8}{a^{10}} = a^2 \times a^{8-10} = a^2 \times a^{-2} = a^{2 + (-2)} = a^0$

Recall that any non-zero number raised to the power of zero is 1, hence: $a^0 = 1$

Therefore, the solution to the problem is $1$.