Reduce the Expression: 8^25 × 7^3 × 10^3 × 5^25 × 5 Step-by-Step

Let's simplify the expression $8^{25} \times 7^3 \times 10^3 \times 5^{25} \times 5$.

Firstly, take note of the terms that we can combine based on their exponents:

• Combine $8^{25}$ and $5^{25}$: Using the property $a^m \times b^m = (a \times b)^m$, we have:
  $8^{25} \times 5^{25} = (8 \times 5)^{25}$.
• The terms $7^3$ and $10^3$ can be combined similarly: $7^3 \times 10^3 = (7 \times 10)^3$.
• Remain aware of the remaining factor of $5$ which does not pair with others.

Putting these together, the expression can be rewritten as:

$(8 \times 5)^{25} \times (7 \times 10)^3 \times 5$

The expression is now fully simplified using the rules of exponents and the indicated product combinations.

Thus, the correct rewritten form of the expression is:

$\left(8\times5\right)^{25}\times\left(7\times10\right)^3\times5$