Lesson: Intermediate Problem Solving - 16t05

The Roman Numeral Question, continued

[Page 16 of 27]

In which of the following pairs are the two numbers equivalent?

I. and
II. and
III. and 243

None
II only
III only
I and II
I, II, and III
Which statement would you evaluate first? Select the radio button for the statement that you might evaluate first, then click Continue.

  Statement I Statement II Statement III

Are the following two numbers equivalent? Select the correct answer and click Continue.

II. and


  Yes No    

Are the following two numbers equivalent? Select the correct answer and click Continue.

III. and 243


  Yes No    

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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