# Algebra II : Simple Exponents

## Example Questions

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### Example Question #198 : Understanding Exponents

Simplify the following expression

Explanation:

### Example Question #199 : Understanding Exponents

Simplify the following expression

Explanation:

### Example Question #1 : Simple Exponents

Solve for x:

Explanation:

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 :

Explanation:

Rewrite in exponential form with a base of :

Solve for by equating exponents:

### Example Question #3 : Simple Exponents

Solve for :

Explanation:

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  ?

Explanation:

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 .

Explanation:

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

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

### Example Question #5 : Simple Exponents

Solve for :

Explanation:

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 :

Explanation:

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.

Evaluate: