### All PSAT Math Resources

## Example Questions

### Example Question #11 : Exponential Operations

If *m* and *n* are integers such that *m* < *n* < 0 and *m*^{2} – *n*^{2} = 7, which of the following can be the value of *m* + *n*?

I. –5

II. –7

III. –9

**Possible Answers:**

I, II and III only

II and III only

I and II only

II only

I only

**Correct answer:**

II only

*m* and *n* are both less than zero and thus negative integers, giving us *m*^{2} and *n*^{2} as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.

### Example Question #11 : Exponential Operations

**Possible Answers:**

**Correct answer:**

To simplify, we can rewrite the numerator using a common exponential base.

Now, we can factor out the numerator.

The eights cancel to give us our final answer.

### Example Question #11 : Exponential Operations

If , then what is ?

**Possible Answers:**

**Correct answer:**

Follow the order of operations by solving the expression within the parentheses first.

Return to solve the original expression.

### Example Question #1 : How To Subtract Exponents

Solve:

**Possible Answers:**

**Correct answer:**

Subtract the denominator exponent from the numerator's exponent, since they have the same base.

Certified Tutor