Final answer:
The expression (3^-6) * (3^4 / 3^0)^2 simplifies to 3^2, which has a value of 9. Hence, the correct answer to the question is c) 9.
Step-by-step explanation:
The question asks to find the value of (3^-6) * (3^4 / 3^0)^2. We will use the properties of exponents to solve the expression:
- First, remember that any number to the power of 0 is 1, so 3^0 = 1.
- Secondly, simplify the inner expression 3^4 / 3^0, which becomes 3^4 / 1, or simply 3^4.
- Third, raise the simplified expression to the second power, so (3^4)^2 is equal to 3^(4*2) or 3^8.
- Finally, multiply 3^-6 by 3^8 to get 3^(8-6), which simplifies to 3^2.
The value of 3^2 is 9, so the correct answer is c) 9.