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(-4p)^4
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This is a law of exponents problem. Since this is a multiplication problem, and a power raised to another power, we multiply the powers.
So for our problem
(-4)^(1 x 4) * p^(1 x 4)
-4^4 * p^4
256p^4
Notice that 256 is positive, this is due to the fact that four negatives multiplied is positive.
Thus this is our final answer 256p^4
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