How to divide exponential variables

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ISEE Upper Level Quantitative Reasoning › How to divide exponential variables

Questions 1 - 10
1

Simplify if .

Explanation

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

Next, expand the denominator.

Simplify by canceling terms.

2

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

3

Solve the following:

Explanation

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

Also, we divide the coefficients like normal.

So, we get

4

Divide the following:

Explanation

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

Now, let’s combine the following:

5

Divide the following::

Explanation

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

Now, let’s divide the following:

6

Simplify:

Explanation

7

Simplify:

Explanation

8

If , simplify:

Explanation

9

Divide the following:

Explanation

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

So, we get

10

Simplify:

Explanation

To simplify, we will use the following formula:

So, given the problem, we get

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