### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Exponential Operations

Simplify:

**Possible Answers:**

**Correct answer:**

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

### Example Question #1 : Exponential Operations

Evaluate:

**Possible Answers:**

**Correct answer:**

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

Now they must be multiplied out before they can be added:

### Example Question #3 : Exponential Operations

Subtract and simplify:

**Possible Answers:**

**Correct answer:**

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #4 : Exponential Operations

Define an operation as follows:

For all real numbers ,

.

Evaluate: .

**Possible Answers:**

**Correct answer:**

, so

### Example Question #2 : Exponential Operations

Subtract and simplify:

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #6 : Exponential Operations

Define an operation as follows:

For all real numbers ,

.

Evaluate: .

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Exponential Operations

Define an operation as follows:

For all real numbers ,

.

Evaluate:

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Exponential Operations

Define as follows:

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #9 : Exponential Operations

Simplify the expresseion:

**Possible Answers:**

The expression is already simplified.

**Correct answer:**

The expression is already simplified.

Variable terms can be combined by adding and subtracting if and only of they are like - that is, if each exponent of each variable is the same. In the given expression, no two exponents are the same. The terms cannot be combined, and the expression is already simplified.

### Example Question #10 : Exponential Operations

Define a function as follows:

Evaluate .

**Possible Answers:**

**Correct answer:**