### All GRE Math Resources

## Example Questions

### Example Question #31 : Algebra

Solve for

**Possible Answers:**

**Correct answer:**

Recall that .

With same base, we can write this equation:

.

By subtracting on both sides, .

### Example Question #32 : Algebra

Solve for .

**Possible Answers:**

**Correct answer:**

Since we can rewrite the expression.

With same base, let's set up an equation of .

By subtracting on both sides, we get .

Take the square root of both sides we get BOTH and .

### Example Question #1 : Exponents And Rational Numbers

Solve for .

**Possible Answers:**

**Correct answer:**

They don't have the same base, however: .

Then . You would multiply the and the instead of adding.

.

### Example Question #2 : Exponents And Rational Numbers

Solve for .

**Possible Answers:**

**Correct answer:**

There are two ways to go about this.

Method

They don't have the same bases however: . Then

You would multiply the and the instead of adding. We have

Divide on both sides to get .

Method :

We can change the base from to

This is the basic property of the product of power exponents.

We have the same base so basically .

### Example Question #10 : Exponents And Rational Numbers

Solve for .

**Possible Answers:**

**Correct answer:**

Since we can write .

With same base we can set up an equation of

Divide both sides by and we get .

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

Solve for .

**Possible Answers:**

**Correct answer:**

We still don't have the same base however:

Then,

.

With same base we can set up an equation of .

Divide both sides by and we get .

### 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:**

Quantity A is greater.

The answer cannot be determined from the information given.

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 #31 : Algebra

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

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 #31 : Algebra

**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.