# College Algebra : Review and Other Topics

## Example Questions

### Example Question #311 : College Algebra

Simplify the following expression.

Explanation:

When multiplying exponential, the exponents always add. While the 2 in the front of the first exponential might throw you off, you may disregard it initially.

Which simplifies to

### Example Question #1 : Real Exponents

Simplify the following expression:

Explanation:

First, we need to simplify the numerator. First term,  can be simplified to . Plugging this back into the numerator, we get

, which simplifies to . Plugging this back into the original equation gives us

, which is simply .

### Example Question #2 : Real Exponents

Solve for :

Explanation:

When like bases with exponents are multiplied, the value of the product's exponent is the sum of both original exponents as shown here:

We can use this common rule to solve for  in the practice problem:

### Example Question #4 : Real Exponents

Solve for :

Explanation:

The product of dividing like bases with exponents is the difference of the numerator and denominator exponents. This is a common rule when working with rational exponents:

We can use this common rule to solve for :

### Example Question #1 : Real Exponents

Solve for :

Explanation:

To solve for , we need all values to have like bases:

Now that all values have like bases, we can solve for :

### Example Question #1 : Real Exponents

Solve for :

Explanation:

To solve for , we want all values in the equation to have like bases:

Now we can solve for :

### Example Question #7 : Real Exponents

Solve for :

Explanation:

To solve for , we want all the values in the equation to have like bases:

Now we can solve for :

### Example Question #1 : Real Exponents

Simplify the following expression.

Explanation:

The original expression can be rewritten as

. Whenever you can a fraction raised to a power, that power gets distributed out to the numerator and denominator. In mathematical terms, the new expression is

, which simply becomes , or

Subtract and simplify:

Explanation:

Find the lease common denominator:

A radical cannot be in the denominator:

### Example Question #2 : Radicals

Find the value of .