To solve the expression 1/2 * 1/3 * x^5 * x^7, we first handle the coefficients. We multiply 1/2 by 1/3, which gives us 1/6. Next, we look at the variable part of the expression. When multiplying variables with the same base, we add their exponents. Here, we have x raised to the power of 5 and x raised to the power of 7. Therefore, we add the exponents: 5 + 7 = 12. This means that x^5 * x^7 simplifies to x^12. Combining both parts, we get the final simplified expression: 1/6 x^12.