# GMAT Math : Understanding exponents

## 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?

is an undefined quantity

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  ?

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?

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

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?

must be an undefined quantity

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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