Final answer:
The product of (3y^-4) and (2y^-4) is calculated by multiplying the coefficients and then adding the exponents of like bases, resulting in the expression 6/y^16.
Step-by-step explanation:
The student asked for the product of (3y-4) multiplied by (2y-4). To find this product, we apply the laws of exponents which state that when we multiply two expressions with the same base, we add the exponents. Here, both expressions have the base y. The exponents are both negative four, so when we add them together we get y-8.
The next step is to multiply the coefficients (the numbers in front of the y terms): 3 times 2 equals 6. So now, our expression looks like 6y-8. According to the rules of exponents, a negative exponent indicates that the base and its exponent should be taken as the reciprocal for positive exponentiation. Therefore, y-8 becomes 1/y8.
Our final product, therefore, is 6/y16 which matches answer choice (b).