ISEE Upper Level Quantitative : How to add exponential variables

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

Example Question #1 : How To Add Exponential Variables

Simplify:

Possible Answers:

The expression cannot be simplified further

Correct answer:

Explanation:

Group and combine like terms :

Example Question #2 : How To Add Exponential Variables

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

Since  and  have different signs,

, and, subsequently,

Therefore, 

This makes (b) the greater quantity.

Example Question #3 : How To Add Exponential Variables

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

(a) 

(b) 

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

Correct answer:

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) 

Possible Answers:

It is impossible to tell from the information given

(a) and (b) are equal

(a) is greater

(b) is greater

Correct answer:

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: 

Possible Answers:

None of the answer choices are correct.

Correct answer:

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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