Simplify the Expression: 7³ × 5² × 7⁴ × 5³ Using Laws of Exponents

Simplify the following equation:

$7^3\times5^2\times7^4\times5^3=$

To solve this problem, we'll use the product of powers property which states $a^m \times a^n = a^{m+n}$.

• Step 1: Simplify the expression by grouping the like bases. The original expression is $7^3 \times 5^2 \times 7^4 \times 5^3$.

• Step 2: Combine the exponents for each base. For base 7: $7^3 \times 7^4 = 7^{3+4} = 7^7$. For base 5: $5^2 \times 5^3 = 5^{2+3} = 5^5$.

• Step 3: Write the simplified expression. After combining the exponents, the expression becomes $7^7 \times 5^5$.

Thus, the solution to the problem is $7^7 \times 5^5$.