How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents?
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Radicals can be also be written as numbers with rational exponents, which allows you to apply the same properties of rational exponents to them.
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First, I will state something from the Law of Indices:
Okay, for example we want to simplify this:
Because of the Law of Indices, we can write these as numbers with rational exponents. (To make it easier for us, let's write 4 as 22)
=223⋅213 (We simplified 226 to 213)
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Remember that when multiplying numbers with the same base, you simply add their exponents. In this case, both numbers have the same base (2).
u see were it says 226 thats a fraction and the number next to it is a fractiom