Question
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Tutor-Verified Answer
Answer
\( x = 3 \)
Solution
We are given the equation: (-6)^x = -216.
Step 1. Notice that (-6)^3 = (-6) × (-6) × (-6).
Step 2. Compute (-6)^3:
(-6)^3 = (-6) × (-6) × (-6) = 36 × (-6) = -216.
Step 3. Since (-6)^3 equals -216, the equation holds true when x = 3.
Thus, the solution is x = 3.
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Simplify this solution Bonus Knowledge
To solve the equation \( (-6)^{x} = -216 \), we can rewrite -216 in terms of base -6. Notice that \( -216 = (-6)^{3} \). So, we can set the exponents equal to each other: \[ x = 3 \] However, keep in mind that when dealing with even and odd powers of negative numbers, if \( x \) is an even integer, the result is positive. Since \( -216 \) is negative, \( x \) must be odd. Therefore, in this case, \( x = 3 \) is indeed the solution because it is odd.
