Simplify the Expression: 6²×6³×3² Using Exponent Rules

Reduce the following equation:

$6^2\times6^3\times3^2=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of exponents with the same base (A)

00:06 equals the same base raised to the sum of the exponents (N+M)

00:09 We'll apply this formula to our exercise, one operation at a time

00:13 We'll maintain the base and add up the exponents

00:21 This is the solution

Step-by-Step Solution

To simplify the expression $6^2 \times 6^3 \times 3^2$ , we will apply the rules for exponents:

Step 1: Identify powers with the same base. Here, we notice that $6^2$ and $6^3$ are powers with the base 6.
Step 2: Use the rule $a^m \times a^n = a^{m+n}$ to combine these powers: $6^2 \times 6^3 = 6^{2+3} = 6^5$ .
Step 3: The term $3^2$ remains unaffected by this operation because its base differs from that of 6. Therefore, it stays as $3^2$ .

Therefore, the simplified form of $6^2 \times 6^3 \times 3^2$ is $6^5 \times 3^2$ .