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

Simplify the following equation:

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

Video Solution

Solution Steps

00:00 Simply

00:04 Let's arrange the exercise so that equal bases are adjacent

00:14 According to laws of exponents, when multiplying powers with the same base (A)

00:17 We get the same base (A) raised to the sum of exponents (M+N)

00:22 Let's use this formula in our exercise

00:26 Let's compare terms according to the formula and simplify

00:31 Let's keep the base

00:35 Let's sum the exponents

00:54 Let's use the same method to simplify the second base

01:17 And this is the solution to the question

Step-by-Step Solution

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 $7^7 \times 5^5$ .