Simplify the Expression: a¹⁰ × b⁵ × a⁻² × b³

First, we'll use the distributive property of multiplication and arrange the algebraic expression according to like bases:

$a^{10}\cdot a^{-2}\cdot b^5\cdot b^3$

From here on we will no longer indicate the multiplication sign, but instead use the conventional writing method where placing terms next to each other means multiplication.

Note that we need to multiply terms with identical bases, so we'll use the appropriate power rule:

$c^m\cdot c^n=c^{m+n}$

Note that this rule can only be used to calculate multiplication between terms with identical bases,

In this problem, there is also a term with a negative exponent, but this doesn't pose an issue regarding the use of the aforementioned power rule. In fact, this power rule is valid in all cases for numerical terms with different exponents, including negative exponents, rational exponents, and even irrational exponents, etc.,

Let's apply it to the problem:

$a^{10}a^{-2}b^5b^3=a^{10-2}b^{5+3}=a^8b^8$

When we dealt separately with terms having equal bases, meaning separately with terms having bases $a$ and $b$

therefore the correct answer is D.