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Here is a walk-through example of how to do a problem like this:
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.
1 : Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Follow the walkthrough above closely; start with simplifying the inside of each set of parentheses, then distribute the power from
the parentheses, then combine the two results into a single fraction.
2 : Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Follow the walkthrough above closely; start with simplifying the inside of each set of parentheses, then distribute the power from
the parentheses, then combine the two results into a single fraction.
3 : Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Follow the walkthrough above closely; start with simplifying the inside of each set of parentheses, then distribute the power from
the parentheses, then combine the two results into a single fraction.
4 : Use rules of exponents to rewrite the following expression without any fractions (using negative exponents if needed).
Follow the walkthrough above closely; start with simplifying the inside of each set of parentheses, then distribute the power from
the parentheses, then combine the two results into a single fraction.
Precalculus Algebra MAC1140