Evaluate (20×5)^7: Solving a Complex Exponent Expression

Choose the expression that corresponds to the following:

$\left(20\times5\right)^7=$

Step 1: We start with the expression $\left(20 \times 5\right)^7$.
Step 2: We'll apply the power of a product rule, which states $(a \times b)^n = a^n \times b^n$. This gives us: $\left(20 \times 5\right)^7 = 20^7 \times 5^7$ .
Step 3: To verify, notice that both $20^7 \times 5^7$ and $5^7 \times 20^7$ involve the same expression due to the commutative property of multiplication. Also, we can rewrite $\left(20 \times 5\right)$ as $100$, leading to another form: $\left(20 \times 5\right)^7 = 100^7$
Thus, both $20^7 \times 5^7$, $5^7 \times 20^7$, and $100^7$ are equivalent expressions for $\left(20 \times 5\right)^7$.

Therefore, the correct answer choice is (d) "All answers are correct."