# GRE Math : How to find a rational number from an exponent

## 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

43                              34

The answer cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

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 #11 : Exponents And Rational Numbers

Quantity A:

Quantity B:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity B is greater.

Explanation:

(–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

Explanation:

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

### Example Question #32 : Algebra

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,

### Example Question #41 : Gre Quantitative Reasoning

Simplify

Explanation:

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

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