Final answer:
The prime factorization of 100q^4s^6 is 2^2 x 5^2 x q^4 x s^6, where the numerical part 100 has been factored into its prime factors and the variables are already in prime factor form.
Step-by-step explanation:
To find the prime factorization of 100q^4s^6, we need to factor the numerical part, 100, and express the variable parts with exponents already in lowest terms. The number 100 is a composite number that can be broken down into prime factors as 22 × 52. As the variables q and s are already raised to a power, we can keep them as they are.
Putting it all together, the prime factorization of 100q^4 s^6 would be 2 * 2 * 5 * 5 * q * q * q * q * s * s * s * s * s * s.
Thus, the prime factorization of the given expression is 2² × 5² × q⁴ × s⁶