GRE Math : How to multiply exponents

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 : How To Multiply Exponents

(b * b* b7)1/2/(b3 * bx) = b5  

If b is not negative then x = ?

Possible Answers:

7

1

–1

–2

Correct answer:

–2

Explanation:

Simplifying the equation gives b6/(b3+x) = b5.  

In order to satisfy this case, x must be equal to –2.

Example Question #2 : How To Multiply Exponents

If〖7/8〗n= √(〖7/8〗5),then what is the value of n?

 

Possible Answers:

1/5

5/2

25

√5

2/5

Correct answer:

5/2

Explanation:

7/8 is being raised to the 5th power and to the 1/2 power at the same time. We multiply these to find n.

Example Question #3 : How To Multiply Exponents

Quantity A:

 (0.5)3(0.5)3

 

Quantity B: 

(0.5)7

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Correct answer:

Quantity A is greater.

Explanation:

When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:


xaxb = xa+b

This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6

Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.

Thus, (0.5)6 > (0.5)7

Example Question #4 : How To Multiply Exponents

For the quantities below, x<y and x and y are both integers.

Please elect the answer that describes the relationship between the two quantities below:

Quantity A

x5y3

 

Quantity B

x4y4

Possible Answers:

Quantity B is greater.

The quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information provided.

Correct answer:

The relationship cannot be determined from the information provided.

Explanation:

Answer: The relationship cannot be determined from the information provided.

Explanation: The best thing to do here is to notice that quantity A is composed of two complex terms with odd exponents. Odd powers result in negative results when their base is negative. Thus quantity A will be negative when either x or y (but not both) is negative. Otherwise, quantity A will be positive. Quantity B, however, has two even exponents, meaning that it will always be positive. Thus, sometimes Quantity A will be greater and sometimes Quantity B will be greater. Thus the answer is that the relationship cannot be determined.

Example Question #5 : How To Multiply Exponents

Simplify: (x3 * 2x4 * 5y + 4y2 + 3y2)/y

Possible Answers:

10x7 + 7y

None of the other answers

10x11 + 7y3

10x7y + 7y2

10x7 + 7y3

Correct answer:

10x7 + 7y

Explanation:

Let's do each of these separately:

x3 * 2x4 * 5y = 2 * 5 * x* x* y = 10 * x7 * y = 10x7y

4y2 + 3y2 = 7y2

Now, rewrite what we have so far:

(10x7y + 7y2)/y

There are several options for reducing this.  Remember that when we divide, we can "distribute" the denominator through to each member.  That means we can rewrite this as:

(10x7y)/y + (7y2)/y

Subtract the y exponents values in each term to get:

10x7 + 7y

Example Question #6 : How To Multiply Exponents

Quantitative Comparison

 

Quantity A: x3/3

Quantity B: (x/3)3

Possible Answers:

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information given.

Quantity A is greater.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

First let's look at Quantity B:

(x/3)3 = x3/27. Now both columns have an xso we can cancel it from both terms. Therefore we're now comparing 1/3 in Quantity A to 1/27 in Quantity B.  1/3 is the larger fraction so Quantity A is greater.

However, if , then the two quantities would both equal 0.  Thus, since the two quantities can have different relationships based on the value of , we cannot determine the relationship from the information given.

Example Question #1 : How To Multiply Exponents

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

 

(23 )2                       (22 )3                  

 

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Correct answer:

The two quantities are equal.

Explanation:

The two quantites are equal. To take the exponent of an exponent, the two exponents should be multiplied.

(2)or 23*2 = 64   

(2)or 22*3 = 64   

Both quantities equal 64, so the two quantities are equal.

Example Question #8 : How To Multiply Exponents

Compare  and .

Possible Answers:

The answer cannot be determined from the information given.

Correct answer:

Explanation:

To compare these expressions more easily, we'll change the first expression to have  in front. We'll do this by factoring out 25 (that is, ) from 850, then using the fact that .

When we combine like terms, we can see that . The two terms are therefore both equal to the same value.

Example Question #471 : Algebra

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

 is always equal to ; therefore, 5 raised to 4 times 5 raised to 5 must equal 5 raised to 9.

 

is always equal to . Therefore, 5 raised to 9, raised to 20 must equal 5 raised to 180.

Example Question #69 : Exponents

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

First, multiply inside the parentheses: .

Then raise to the 7th power: .

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