# ISEE Upper Level Math : Variables and Exponents

## Example Questions

### Example Question #51 : Variables And Exponents

Simplify:

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 .

Simplify:

Explanation:

### Example Question #53 : Variables And Exponents

Simplify the following expression:

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 #54 : Variables And Exponents

Simplify the following:

Explanation:

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

So, we can write the problem like this:

### Example Question #55 : Variables And Exponents

Combine the following:

Explanation:

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

Now, let’s combine the following:

### Example Question #56 : Variables And Exponents

Combine the following:

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 #57 : Variables And Exponents

Simplify:

Explanation:

To simplify, we will use the following formula:

So, given the problem, we get

### Example Question #58 : Variables And Exponents

Combine the following:

Explanation:

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

So, we get

### Example Question #59 : Variables And Exponents

Simplify the following expression:

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.

### Example Question #60 : Variables And Exponents

Multiply the following: