Simplify the Expression: 2^10 × 3^6 × 2^5 × 3^2 Using Power Rules

Simplify the following equation:

$2^{10}\times3^6\times2^5\times3^2=$

To solve this problem, we'll simplify the expression $2^{10} \times 3^6 \times 2^5 \times 3^2$ using the rules of exponents. Here are the steps:

• Step 1: Apply the product of powers property to the base 2 terms. The expression $2^{10} \times 2^5$ simplifies to:

  $2^{10+5} = 2^{15}$

• Step 2: Apply the product of powers property to the base 3 terms. The expression $3^6 \times 3^2$ simplifies to:

  $3^{6+2} = 3^8$

• Step 3: Combine the simplified terms to form the complete simplified expression:

  $2^{15} \times 3^8$

Therefore, the simplified form of the equation is $2^{15} \times 3^8$.