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# Evaluating radicals and integer exponents

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Author: Jesus Gonzalez

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Tutorial

## What we know

We know how to deal with positive whole number exponents

Because the two terms shared the same base, we were able to combine them through multiplication. The net result is that multiplying the whole terms leads to adding the exponents.

## Negative Exponents

We can apply what we already knew about positive exponents and apply it to negative exponents.

should equal since we noticed before that exponents can just be added together when they have the same base.

And we should get

Notice that  as well from what we knew before. So the key idea to take away here is that

Or more generally:  where a and b are real numbers.

## Rational Exponents

The rule we've been relying on is that when multiplying two term, if the bases match you can add the exponents to combine those terms.

Well now we have to consider something like  or

Since , we would like to equal , since that would agree with the pattern we've noticed so far. This is very similar to what we've learned about roots.

So the general rule to pull from this is that , or more generally: , where a and b are real numbers.

note: When working with numerator that are not 1, you can apply the rules we've learned about exponents on exponents, to simplify something like into or

## Now you're ready for the quiz

Take some time now and consider these 4 questions. Feel free to review what we've discussed.

Once you're done it's time for the Exit Ticket: Here

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