Final answer:
The equivalent expression to (1/16)^-4 is (16)^4, as negative exponents indicate the reciprocal of the base raised to the positive exponent.
Step-by-step explanation:
The student is asking which expression is equivalent to (1/16)^-4. The key to solving this problem is understanding how negative exponents work. According to the rules of exponents, a negative exponent indicates that the number should be in the denominator when it's expressed as a positive exponent. So, x^-n is the same as 1/x^n. This means that (1/16)^-4 is equivalent to (16)^4 because the negative exponent flips the base from 1/16 to 16 before raising it to the power of 4.
Now, considering the provided options, the correct transformation of (1/16)^-4 is indeed (16)^4. The other options do not represent this transformation correctly. The value of (16)^4 is 16 multiplied by itself 4 times, which simplifies to 256² or 65536. Therefore, the equivalent expression to (1/16)^-4 is (16)^4.