Reduce the Expression: 8^(3x) × 8^(3y) × 8^(2y+x)

To solve this problem, let's simplify the expression $8^{3x} \times 8^{3y} \times 8^{2y+x}$ using exponent rules:

Step 1: Identify the exponents in each term:
- The first term is $8^{3x}$ with an exponent of $3x$.
- The second term is $8^{3y}$ with an exponent of $3y$.
- The third term is $8^{2y+x}$ with an exponent of $2y+x$.

Step 2: Apply the multiplication of powers rule:
Since all terms have the same base of 8, add the exponents: $(3x) + (3y) + (2y + x)$.

Step 3: Simplify the expression:
Adding the terms in the exponent gives us: $3x + 3y + 2y + x = 4x + 5y$.

Therefore, the simplified expression is $8^{4x+5y}$.