Answer 1:
Negative 1 raised to an even number, 30 in this case, is positive and equals 1. Think of multiplying 1 thirty times! The answer is still 1.
\[ (1)^{30} = 1\]
The second part is negative 2 raised to the power of negative 4. Remember that a negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. So we get:
\[ (2)^{4} = (\frac{1}{2})^{4} = \frac{1}{16}\]
The final answer is:
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