### All GRE Math Resources

## Example Questions

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

Quantitative Comparison

Quantity A:

Quantity B:

**Possible Answers:**

Quantity A is greater.

The two quantities are equal.

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 4^{5} * 4^{–3 }= 4^{5+(–3)} = 4^{2}. In Quantity B, we subtract the exponents because the operation is division, so 4^{5} / 4^{–}^{3 }= 4^{5–(–3)} = 4^{8}. We don't have to finish multiplying out the exponents to see that Quantity B is greater.

### Example Question #2 : Exponential Ratios

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, .