# 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 #1 : 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.

(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.

It is impossible to tell from the information given.

(b) is greater.

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 : How To Add Exponential Variables Which is the greater quantity?

(a) (b) (b) is greater

It is impossible to tell from the information given

(a) is greater

(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 #5 : How To Add Exponential Variables

Assume all variables to be nonzero.

Simplify:    None of the answer choices are correct. None of the answer choices are correct.

Explanation:

Any nonzero expression raised to the power of 0 is equal to 1. Therefore, .

None of the given expressions are correct.

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