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Mathematical Expression Editor
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Practice for properties of exponentials.
How You Can (And Should) Get More Practice!
Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason
you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete
additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight
forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for
you.
Theoretically Easier Difficulty Problem
Remember that you need to expand the outside power to every term when the inside is in factored form.
Recall that negative exponents means you can flip the fraction. This also means that, if you want to rewrite a term that is in the
denominator as a term in the numerator (for the answer requirement) you can do so by making the exponent
negative!
Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Theoretically Medium Difficulty Problem
It can help to simplify the inside of the fractions fully before doing anything else, as it can dramatically cut down the amount
of computation and room for error in future steps.
Remember that you need to expand the outside power to every term when the inside is in factored form.
Recall that negative exponents means you can flip the fraction. This also means that, if you want to rewrite a term that is in the
denominator as a term in the numerator (for the answer requirement) you can do so by making the exponent
negative!
Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Theoretically Harder Difficulty Problem
If you want a walk-through example of how to do problems like these (or at least the hard version) click the arrow to the right to
expand the walk-through!
Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if
needed):
Solution: First, we should try to simplify the parts inside the large parentheses. Keep in mind this means
we will need to do a bunch of algebra and our last line is likely to involve a ton of cancellation, so remember to
use all the rules to combine exponentials with the same base to see how the below happens (especially the last
step!)
Step 1: Invert the bottom fractions and multiply
Step 2: Multiply straight across
Step 3: Combine like terms to simplify.
Next we want to distribute the large power to each of the terms inside the parentheses. We can do this only
because everything inside is being multiplied! In essence, the inside is factored, so we can distribute the outer power.
From previous work.
Distribute Power.
(You can also distribute the separately from the in the power in the second factor. Essentially you can just “flip” the fraction and make the into a and then distribute the to each term. Either way is perfectly correct!)
Multiple Straight Across.
Simplify powers using Exponential Properties.
Rewrite using negative exponents to avoid having a fraction.
The hardest part of tackling large problems like this, is don’t get intimidated! It’s the same as the previous problem,
just with more terms - so do it the same way as the last one, just take your time and work through it slowly and
carefully.
It can help to simplify the inside of the fractions fully before doing anything else, as it can dramatically cut down the amount of
computation and room for error in future steps.
Remember that you need to expand the outside power to every term when the inside is in factored form.
Recall that negative exponents means you can flip the fraction. This also means that, if you want to rewrite a term that is in the
denominator as a term in the numerator (for the answer requirement) you can do so by making the exponent
negative!
Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)