### All Algebra II Resources

## Example Questions

### Example Question #198 : Understanding Exponents

Simplify the following expression

**Possible Answers:**

**Correct answer:**

### Example Question #199 : Understanding Exponents

Simplify the following expression

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Simple Exponents

Solve for x:

**Possible Answers:**

**Correct answer:**

Solve for x:

**Step 1: Represent ** **exponentially with a base of**

, therefore

**Step 2: Set the exponents equal to each other and solve for x**

### Example Question #2 : Simple Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

Rewrite in exponential form with a base of :

Solve for by equating exponents:

### Example Question #3 : Simple Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

Represent in exponential form using a base of :

Solve for by equating exponents:

### Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

How many perfect squares satisfy the inequality ?

**Possible Answers:**

**Correct answer:**

The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since . The largest can be found by noting that ; this makes the greatest perfect square in this range.

Since the squares of the integers from 10 to 31 all fall in this range, this makes perfect squares.

### Example Question #4 : Simple Exponents

Simplify .

**Possible Answers:**

**Correct answer:**

To solve this expression, remove the outer exponent and expand the terms.

By exponential rules, add all the powers when multiplying like terms.

The answer is:

### Example Question #5 : Simple Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

The first step in solving for x is to simplify the right side:

.

Next, we can re-express the left side as an exponential with 2 as the base.

Now set the new left side equal to the new right side.

With the bases now being the same, we can simply set the exponents equal to each other.

### Example Question #6 : Simple Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

To solve for x, we need to simplify both sides in order to make the equation simpler to solve.

can be rewritten as , and can be written as .

Setting the two sides equal to each other gives us

Since the bases are the same we can set the exponents equal to each other.

### Example Question #7 : Simple Exponents

Evaluate:

**Possible Answers:**

**Correct answer:**

is expanded to .

We will simply multiply the values in order to get the answer: