Expand the Expression: Calculate 8^10 Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Identify the base and exponent given in the expression
• Step 2: Choose an appropriate combination of exponents for the expansion
• Step 3: Verify the selected combination by checking it matches the rule $a^x \times a^y \times a^z = a^{10}$

Now, let's work through each step:
Step 1: We start with the expression $8^{10}$. Our goal is to express this as a product of three powers of 8 that sum to the same exponent.
Step 2: Using the exponent addition rule, we need to find three exponents $a, b,$ and $c$ such that $8^a \times 8^b \times 8^c = 8^{10}$. One possible approach is to try combinations that could plausibly sum to 10. For example, let’s choose $a = 3$, $b = 3$, $c = 4$. Observing that $3 + 3 + 4 = 10$, a valid distribution can be $8^3 \times 8^3 \times 8^4$.
Step 3: Verify if this aligns with the multiplication of powers: $8^3 \times 8^3 \times 8^4 = 8^{3+3+4} = 8^{10}$, confirming that this product is indeed equivalent to $8^{10}$.

Therefore, the correct expanded form of $8^{10}$ is $8^3\times8^3\times8^4$, corresponding to answer choice 2.