Reduce the Expression: 7⁶ × 13² × 4² × 8⁷ × 9² Using Laws of Exponents

Let's solve the problem by following these steps:

Step 1: Identify terms that share a common power. We have $13^2$, $4^2$, and $9^2$, all raised to 2.

Step 2: Use the power of a product rule: $(a \times b \times c)^m = a^m \times b^m \times c^m$.

Step 3: Combine these terms: $13^2 \times 4^2 \times 9^2 = (13 \times 4 \times 9)^2$.

Step 4: Substitute back into the original expression:
$7^6 \times 13^2 \times 4^2 \times 8^7 \times 9^2 = 7^6 \times (13 \times 4 \times 9)^2 \times 8^7$.

Therefore, the expression reduces to $7^6 \times (13 \times 4 \times 9)^2 \times 8^7$.