GRE Math : How to subtract exponents

Study concepts, example questions & explanations for GRE Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #515 : Algebra

Simplify: 32 * (423 - 421)

Possible Answers:

4^4

3^3 * 4^21

3^3 * 4^21 * 5

3^21

None of the other answers

Correct answer:

3^3 * 4^21 * 5

Explanation:

Begin by noting that the group (423 - 421) has a common factor, namely 421.  You can treat this like any other constant or variable and factor it out.  That would give you: 421(42 - 1). Therefore, we know that:

32 * (423 - 421) = 32 * 421(42 - 1)

Now, 42 - 1 = 16 - 1 = 15 = 5 * 3.  Replace that in the original:

32 * 421(42 - 1) = 32 * 421(3 * 5)

Combining multiples withe same base, you get:

33 * 421 * 5

Example Question #1 : How To Subtract Exponents

Quantitative Comparison

Quantity A: 64 – 32

Quantity B: 52 – 42

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined from the information given.

Correct answer:

Quantity A is greater.

Explanation:

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

Example Question #2 : How To Subtract Exponents

, and  is odd.

Quantity A: 

Quantity B: 

 

Possible Answers:

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

Correct answer:

Quantity A is greater.

Explanation:

The first thing to note is the relationship between (–b) and (1 – b):

 (–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: