# GRE Math : Algebra

## Example Questions

### Example Question #31 : Algebra

Solve for

Explanation:

Recall that

With same base, we can write this equation:

By subtracting  on both sides,

### Example Question #32 : Algebra

Solve for .

Explanation:

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 .

Explanation:

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

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

Solve for .

Explanation:

Method

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

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 .

Explanation:

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 .

Explanation:

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

43                              34

Quantity A is greater.

The answer cannot be determined from the information given.

Quantity B is greater.

The two quantities are equal.

Quantity B is greater.

Explanation:

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

4is 4 * 4 * 4 = 64

34 is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

### Example Question #31 : Algebra

Quantity A:

Quantity B:

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

Quantity B is greater.

Explanation:

(–1) 137= –1

–1 < 0

(–1) odd # always equals –1.

(–1) even # always equals +1.

### Example Question #31 : Algebra

Explanation:

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?

Explanation:

Let's all convert the bases to .

This one may be intimidating but .

Therefore,