ISEE Upper Level Math : Variables and Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #15 : How To Multiply Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

First, simplify all of the exponents. When the exponent is outside of the parantheses, multiply it by the exponents inside so that you get: . Multiply so that you get 27. Then, multiply like terms. First, multilpy 2 by 27 so that you get 54. Then, multiply the x terms. Remember, when bases are the same, add the exponents: . Then, multiply the y terms: . Then, multiply all of the terms together so that you get .

Example Question #16 : How To Multiply Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #17 : How To Multiply Exponential Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

To combine these, we need to multiply our coefficients and our variables. 

First, multiply the coefficients 

Next, multiply our variables by adding the exponent:

So, we put it all together to get:

Example Question #18 : How To Multiply Exponential Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

When multiply variables with exponents, we will use the following formula:

 

So, we can write the problem like this:

Example Question #21 : How To Multiply Exponential Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To combine variables with exponents, we will use the following formula:

 

Now, let’s combine the following:

Example Question #22 : How To Multiply Exponential Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

When combining variables with exponents, we can only combine like variables.

When multiply variables with exponents, we add the exponents.  In other words:

 

So, we get

Example Question #117 : Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

To simplify, we will use the following formula:

 

So, given the problem, we get

Example Question #23 : How To Multiply Exponential Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To multiply terms with exponents, we will use the following formula:

 

So, we get

 

 

 

Example Question #121 : Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

Let's begin with the first term.

Because we are raising the whole part to the third, we need to cube each piece, the 4 and the x squared.

Next, simply add our two terms to get our answer

Example Question #122 : Variables

Multiply the following:

Possible Answers:

Correct answer:

Explanation:

To multiply like variables with exponents, we will use the following formula:

 

So, we get

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