Compare Powers: Evaluating 2³×2⁴×2⁸ and 2²×2³×2¹⁰

To solve this problem, we'll apply the multiplication of powers rule, which states that for the same base $a$, $a^m \times a^n = a^{m+n}$. Let's simplify each expression:

For the left side:

• $2^3 \times 2^4 \times 2^8$
• Add the exponents since the bases are the same: $3 + 4 + 8 = 15$
• The simplified form is $2^{15}$

For the right side:

• $2^2 \times 2^3 \times 2^{10}$
• Add the exponents as well: $2 + 3 + 10 = 15$
• The simplified form is $2^{15}$

Now, comparing the two sides: $2^{15}$ and $2^{15}$.

Since both are the same power of 2, we conclude that:

The correct sign to insert is $=$.

Therefore, the solution to the problem is $\boxed{=}$.