# ISEE Upper Level Math : Variables and Exponents

## Example Questions

### Example Question #1012 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Multiply the following:

Explanation:

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

Now, let’s combine the following:

### Example Question #121 : Variables

Solve the following:

Explanation:

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

Also, we will multiply coefficients like normal.

So, we get

### Example Question #1014 : Isee Upper Level (Grades 9 12) Mathematics Achievement

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 #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following:

Explanation:

To divide a variable with an exponent, you can write out all the multiplies, which for this question would look like:

Then cancel out the matching p's, leaving:

Or, if the top and bottom are the same variable, you can simply subtract the bottom exponent from the top exponent.

### Example Question #61 : Variables And Exponents

Simplify the following:

Explanation:

To divide variables with exponents, either:

Write out the multiplies, then reduce

or subtract the bottom exponent from the top, like so

Remember, negative exponent means dividing.  would also be correct, but you should know that is equivalent to

If , simplify:

Explanation:

Simplify:

Explanation:

### Example Question #5 : How To Divide Exponential Variables

Simplify if .

Explanation:

Start by factoring the numerator. can be removed from each term.

Next, expand the denominator.

Simplify by canceling terms.

### Example Question #6 : How To Divide Exponential Variables

Simplify:

Explanation:

In the denominator, apply the exponent to the terms in parentheses.

Terms with negative exponents can be inverted within the fraction to eliminate the negative.

Simplify by canceling variables and mulitplying.

Simplify: