simplify -4^6
-4^6
= -(4*4*4*4*4*4)
= -4096
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To simplify -4^6, you need to follow the order of operations, also known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
In this case, you only have an exponent to deal with. The exponent is 6, so you raise -4 to the power of 6. However, we also need to consider the negative sign in front of the 4.
If you simply calculate -4^6 without considering the order of operations, you would get a different answer than intended. Let's break it down step by step:
1. Calculate the exponent: (-4)^6
This means you multiply -4 by itself six times.
(-4)^6 = (-4) × (-4) × (-4) × (-4) × (-4) × (-4) = 4096
2. Apply the negative sign:
Since the negative sign is in front of the base (-4), we need to multiply the result by -1.
-4^6 = -1 × 4096 = -4096
Therefore, the simplified form of -4^6 is -4096.