College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #311 : College Algebra

Simplify the following expression.

Possible Answers:

Correct answer:

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

Our final answer is 

Example Question #1 : Real Exponents

Simplify the following expression:

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 

 

Example Question #1 : Adding And Subtracting Radicals

Subtract and simplify:

Possible Answers:

Correct answer:

Explanation:

Find the lease common denominator: 

A radical cannot be in the denominator:

 

 

Example Question #2 : Radicals

Find the value of .

Possible Answers:

Correct answer:

Explanation:

To solve this equation, we have to factor our radicals.  We do this by finding numbers that multiply to give us the number within the radical. 

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

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