GMAT Math : Understanding exponents

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #81 : Exponents

 is the additive inverse of the multiplicative inverse of  is the additive inverse of the multiplicative inverse of . Which of the following is equal to the expression

regardless of the values of the variables?

Possible Answers:

 is an undefined quantity

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0; the multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1.

Let  be the multiplicative inverse of . Then 

, or, equivalently, .

 is the additive inverse of this number, so

By similar reasoning, , and

Example Question #1186 : Problem Solving Questions

Which of the following is equal to  ?

Possible Answers:

Correct answer:

Explanation:

Divide:

Substitute:

 

 

Example Question #81 : Understanding Exponents

 is the additive inverse of  is the multiplicative inverse of . Which of the following is equal to the expression

regardless of the values of the variables?

Possible Answers:

 must be an undefined quantity.

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since  is the additive inverse of 

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since  is the multiplicative inverse of , then 

, or .

It follows that

.

0 raised to any nonzero power is equal to 0, and  must be nonzero, so

, the correct response.

Example Question #82 : Understanding Exponents

 is the additive inverse of  is the additive inverse of . Which of the following is equal to the expression

regardless of the values of the variables?

Possible Answers:

 must be an undefined quantity

Correct answer:

 must be an undefined quantity

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since  is the additive inverse of  and  is the additive inverse of 

and 

,

which is an undefined expression.

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