# GMAT Math : Understanding exponents

## Example Questions

### Example Question #91 : Algebra

Which of the following is a true statement?

Explanation:

### Example Question #1172 : Problem Solving Questions

Express  in terms of .

Explanation:

### Example Question #71 : Exponents

Express  in terms of .

Explanation:

### Example Question #71 : Exponents

The first and third terms of a geometric sequence are  and , in that order. Give the eighth term.

(Assume  is positive.)

Explanation:

Let  be the common ratio of the geometric sequence. Then the third term is  times the first, so

and

.

The eighth term of the sequence is

### Example Question #72 : Exponents

Simplify:

Explanation:

To solve, we must first simplify the negative exponents by shifting them to the other side of the fraction:

Then we can simply the multiplied like bases by adding their exponents:

### Example Question #73 : Exponents

Explanation:

First we can simplify the numerator's parentheses by adding the like bases' exponents:

We can then simplify the numerator further by multiplying the base's exponent by the exponent to which it is raised:

We can then subtract the denominator's exponent from the numerator's:

### Example Question #74 : Exponents

Simplify the following expression:

Explanation:

Simplify the following expression:

Let's begin by simplifying the fraction. Recall that when dividing exponents of similar base, we need to subtract the exponents. We can treat the 343 and the 49 just like regular fractions.

Note that then we perform the subtraction step to get our final answer:

### Example Question #1181 : Problem Solving Questions

is the multiplicative 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

Explanation:

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 .

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

It follows that

Any nonzero number raised to the power of 0 is equal to 1. Therefore,

, the correct choice.

### Example Question #75 : 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?

is 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

, or

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

.

It follows that

, the correct response.

### Example Question #71 : Understanding Exponents

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

regardless of the values of the variables?

is an undefined quantity.

Explanation:

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

.

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

, or .

It follows that

, the correct response.