# College Algebra : Review and Other Topics

## Example Questions

### Example Question #1 : Rational Exponents

Evaluate.

Possible Answers:

Correct answer:

Explanation:

Exponents raised to a power of <1 can be written as the root of the denominator.

So:

Recall that a square root can give two answers, one positive and one negative.

### Example Question #7 : Rational Exponents

Evaluate

Possible Answers:

Correct answer:

Explanation:

The denominator of the exponent "N" is the same as the "N" root of that number.

So

### Example Question #8 : Rational Exponents

Evaluate

Possible Answers:

Correct answer:

Explanation:

This appears more complicated than it is.

is really just where

and

Re-written this equation looks like

### Example Question #9 : Rational Exponents

Evaluate

Possible Answers:

Correct answer:

Explanation:

can be seen as , in a scientific calculator use the  button where .

### Example Question #1 : Rational Exponents

Evaluate the given rational exponent:

Possible Answers:

Correct answer:

Explanation:

Rational exponents can be simplified by following this common rule:

We can apply this concept to the given value in order to evaluate:

### Example Question #31 : Review And Other Topics

Solve for :

Possible Answers:

Correct answer:

Explanation:

We can use the given property of rational exponents to solve for :

### Example Question #11 : Rational Exponents

Solve for :

Possible Answers:

Correct answer:

Explanation:

We can use the given property of rational exponents to solve for :

### Example Question #12 : Rational Exponents

Evaluate:

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to understand what the fractional value in the exponent is.

A fractional exponent, , tells us that we must take the th root of the number.

In this case, we have , so we will take the 4th root of .

Step 2: Calculate...

The answer is .

### Example Question #34 : Review And Other Topics

Simplfy:

Possible Answers:

Correct answer:

Explanation:

Treat this with regular exponent rules.

### Example Question #35 : Review And Other Topics

Simplify:

Possible Answers:

The answer is not present.

Correct answer:

Explanation: