Subjects algebra

Power Expression 14D184

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1. The problem is to express the product $(-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4)$ as a power. 2. When the same number is multiplied by itself multiple times, it can be written as an exponent or power. The general form is $a^n$ where $a$ is the base and $n$ is the exponent representing how many times $a$ is multiplied by itself. 3. Here, the base is $-4$ and it is multiplied 6 times, so the expression can be written as: $$(-4)^6$$ 4. To evaluate $(-4)^6$, note that an even power of a negative number results in a positive number because multiplying two negatives gives a positive. 5. Calculate step-by-step: $$(-4)^6 = (-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4)$$ $$= ((-4) \times (-4)) \times ((-4) \times (-4)) \times ((-4) \times (-4))$$ $$= (16) \times (16) \times (16)$$ $$= 16 \times 16 \times 16$$ $$= 256 \times 16$$ $$= 4096$$ 6. Therefore, the final answer is: $$(-4)^6 = 4096$$