In which of the following pairs are the two numbers equivalent?
I. and II. and III. and 243
II. and
III. and 243
Since the expression on the left has a common base, we can add the exponents to simplify: . These numbers are equivalent, and Choice (C) is correct.
At this point we could simply choose (C) and move on. We didn't even need to evaluate Statement I. This is not unusual, and is one reason why you should always approach Roman Numeral problems systematically.
If we had evaluated Statement I, we would've found that the numbers are not equal.
When raising a power to another power, we multiply the exponents:
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