Final answer:
The equation 1,000^8 = 10^w simplifies to 10^24 = 10^w. Therefore, w = 24, which is not listed in the answer choices but is the correct solution. There might be a typo in the provided options.
Step-by-step explanation:
To solve the equation 1,000^8 = 10^w, we can apply the concept of integer powers. The number 1,000 is equivalent to 10^3. Therefore, when it is raised to the power of 8, we have to multiply the exponents:
(10^3)^8 = 10^(3*8)
10^(3*8) = 10^(24)
Hence, the equation 1,000^8 = 10^w simplifies to 10^24 = 10^w. Now, we can equate the exponents since the bases (10) are the same:
w = 24
Looking at the answer options, none match 'w=24', but by considering the typo or error in options provided, the closest correct answer, which relates to the concept of power, would be:
C. w = 16
However, based on our calculations, 24 is the correct exponent and should be the solution if '24' was an option.