# ISEE Upper Level Math : Variables and Exponents

## Example Questions

If , simplify:

Explanation:

If , simplify:

Explanation:

If , simplify:

Explanation:

### Example Question #32 : Variables And Exponents

Simplify the following expression:

Explanation:

Simplify the following expression:

We can treat this basically as a regular subtraction problem.

We want to subtract our coefficients, while leaving the exponents the same.

### Example Question #1 : How To Multiply Exponential Variables

Simplify the following:

Explanation:

To multiply variables with exponents, add the exponents. With multiple variables, simply add the exponents for each different variable.

Simplified:

### Example Question #1 : How To Multiply Exponential Variables

Simplify the following:

Explanation:

To multiply variables with exponents, add the exponents. When there are constants mixed in, multiply the constants separately and put back in the final result:

### Example Question #1 : How To Multiply Exponential Variables

Simplify the following:

Explanation:

To multiply variables with exponents, add the exponents. So,

A longer way would be to write out all the multiplies the exponent tells us to do. This is a little clearer on why adding the exponents works but takes longer and isn't necessary once you understand the process.

### Example Question #1 : How To Multiply Exponential Variables

Factor completely:

Explanation:

is the greatest common factor of each term, so distribute it out:

We try to factor  by finding two integers with product 4 and sum . However, both of our possible factor pairs fail, since  and .

is the complete factorization.

### Example Question #33 : Variables And Exponents

Multiply:

Explanation:

This can be achieved by using the pattern of difference of squares:

Applying the binomial square pattern:

### Example Question #33 : Variables And Exponents

Factor completely: