### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Divide Exponential Variables

Half of one hundred divided by five and multiplied by one-tenth is __________.

**Possible Answers:**

2

1

10

5

**Correct answer:**

1

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

### Example Question #2 : How To Divide Exponential Variables

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #3 : How To Divide Exponential Variables

Simplify:

**Possible Answers:**

**Correct answer:**

Break the fraction up and apply the quotient of powers rule:

### Example Question #4 : How To Divide Exponential Variables

Simplify:

**Possible Answers:**

**Correct answer:**

To simplify this expression, look at the like terms separately. First, simplify . This becomes . Then, deal with the . Since the bases are the same and you're dividing, you can subtract exponents. This gives you Since the exponent is positive, you put in the numerator. This gives you a final answer of .

### Example Question #5 : How To Divide Exponential Variables

is a negative number.

Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

(a) and (b) are equal

(b) is the greater quantity

It is impossible to determine which is greater from the information given

(a) is the greater quantity

**Correct answer:**

(b) is the greater quantity

A negative number raised to an odd power is negative; a negative number raised to an even power is positive. It follows that is negative and is positive. Also, the reciprocal of a nonzero number assumes the same sign as the number itself, so the reciprocal of is positive and that of is negative. It follows that the reciprocal of is the greater of the two.

### Example Question #6 : How To Divide Exponential Variables

Simplify:

**Possible Answers:**

**Correct answer:**

Break the fraction up and apply the quotient of powers rule: