Expand the Expression: Calculate 8^4 Step by Step

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

• Step 1: Understand the given information, which is the expression $8^4$.
• Step 2: Check each choice to see if it is a valid decomposition of $8^4$.
• Step 3: Validate each decomposition by applying the formula $a^m \times a^n = a^{m+n}$.

Now, let's work through each step:
Step 1: The given expression is $8^4$. We need to expand it using the properties of exponents.
Step 2: Check each choice:
- Choice 1: $8^1 \times 8^3$. According to the law $a^m \times a^n = a^{m+n}$, this gives $8^{1+3} = 8^4$. Correct.
- Choice 2: $8^2 \times 8^2$. Similarly, $8^{2+2} = 8^4$. Correct.
- Choice 3: $8^3 \times 8^1$. This gives $8^{3+1} = 8^4$. Correct.
Step 3: All choices decompose $8^4$ correctly into powers of 8 that multiply back to the original value, confirming their validity.

Therefore, the solution to the problem is all answers are correct.