# ISEE Upper Level Quantitative : How to add exponential variables

## Example Questions

### Example Question #1 : Variables And Exponents

Simplify:

The expression cannot be simplified further

Explanation:

Group and combine like terms :

### Example Question #2 : Variables And Exponents

Which is the greater quantity?

(a)

(b)

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(b) is greater.

Explanation:

Since  and  have different signs,

, and, subsequently,

Therefore,

This makes (b) the greater quantity.

### Example Question #1 : How To Add Exponential Variables

Assume that  and  are not both zero. Which is the greater quantity?

(a)

(b)

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

It is impossible to tell from the information given.

Explanation:

Simplify the expression in (a):

Therefore, whether (a) or (b) is greater depends on the values of  and , neither of which are known.

### Example Question #4 : Variables And Exponents

Which is the greater quantity?

(a)

(b)

(b) is greater

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

It is impossible to tell from the information given

Explanation:

We give at least one positive value of  for which (a) is greater and at least one positive value of  for which (b) is greater.

Case 1:

(a)

(b)

Case 2:

(a)

(b)

Therefore, either (a) or (b) can be greater.

### Example Question #2 : How To Add Exponential Variables

Assume all variables to be nonzero.

Simplify:

None of the answer choices are correct.