GRE Math : How to find a ratio of exponents

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find A Ratio Of Exponents

Quantitative Comparison

Quantity A: 

Quantity B:

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

Correct answer:

Quantity B is greater.


In Quantity A, we add the exponents because the operation is multiplication, so 45 * 4–3 = 45+(–3) = 42. In Quantity B, we subtract the exponents because the operation is division, so 45 / 4= 45–(–3) = 48. We don't have to finish multiplying out the exponents to see that Quantity B is greater.

Example Question #2 : How To Find A Ratio Of Exponents

If  and  are both rational numbers and , what is ?

Possible Answers:

Correct answer:


This question is asking you for the ratio of m to n.  To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent.  The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.

And, would you look at that. .  Therefore, .

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