ISEE Upper Level Math : How to divide exponential variables

Example Questions

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Example Question #1 : How To Divide Exponential Variables

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 #2 : How To Divide Exponential Variables

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.

Example Question #7 : How To Divide Exponential Variables

Simplify:

Explanation:

Break up the fraction into components with like-terms.

Simplify by combining exponents. Remember that exponents in the denominator will become negative.

Finally, put any negative exponent terms into the denominator.

Simplify:

Explanation:

Example Question #9 : How To Divide Exponential Variables

Divide the following:

Explanation:

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

Now, let’s combine the following:

Example Question #10 : How To Divide Exponential Variables

Divide the following:

Explanation:

When dividing variables, we can only divide like variable.

Also, when dividing variables with exponents, we subtract the exponents.  In other words:

So, we get

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