# 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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