### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Find A Rational Number From An Exponent

**Quantitative Comparison:** Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.

**Quantity A Quantity B**

4^{3 }3^{4}

**Possible Answers:**

The answer cannot be determined from the information given.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

**Correct answer:**

Quantity B is greater.

In order to determine the relationship between the quantities, solve each quantity.

4^{3 }is 4 * 4 * 4 = 64

3^{4} is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

### Example Question #11 : Exponents And Rational Numbers

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined from the information given.

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

**Correct answer:**

Quantity B is greater.

(–1) ^{137}= –1

–1 < 0

(–1) ^{odd #} always equals –1.

(–1) ^{even #} always equals +1.

### Example Question #1 : How To Find A Rational Number From An Exponent

**Possible Answers:**

**Correct answer:**

Anything raised to negative power means over the base raised to the postive exponent.

### Example Question #12 : Exponents And Rational Numbers

Which of the following is not the same as the others?

**Possible Answers:**

**Correct answer:**

Let's all convert the bases to .

This one may be intimidating but .

Therefore,

is not like the answers so this is the correct answer.

### Example Question #1 : How To Find A Rational Number From An Exponent

Simplify

**Possible Answers:**

**Correct answer:**

Whenever you see lots of multiplication (e.g. exponents, which are notation for repetitive multiplication) separated by addition or subtraction, a common way to transform the expression is to factor out common terms on either side of the + or - sign. That allows you to create more multiplication, which is helpful in reducing fractions or in reducing the addition/subtraction to numbers you can quickly calculate by hand as you'll see here.

So let's factor a .

We have .

And you'll see that the addition inside parentheses becomes quite manageable, leading to the final answer of .