Final answer:
To rewrite 16r^2s^2 as a power of a product, we need to break down the expression into its prime factors and simplify it. The final answer will be in the form of (2 * r * s)^2.
Step-by-step explanation:
This question is asking us to rewrite 16r^2s^2 as a power of a product. In order to do this, we need to break down the expression 16r^2s^2 into its prime factors. The prime factors of 16 are 2 * 2 * 2 * 2 and the prime factors of r^2 and s^2 are r * r and s * s, respectively.
So, we can rewrite 16r^2s^2 as (2 * 2 * 2 * 2) * (r * r) * (s * s). This can be further simplified as 2^4 * r^2 * s^2, which can be expressed as a power of a product as 2^4 * r^2 * s^2 = (2 * r * s)^2.