# week 7 lec1 - RADICAL EXPRESSIONS Simplifying Recall the...

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RADICAL EXPRESSIONS – Simplifying Recall the power rule for exponents states (am) n= am*n. That means if given (x2)5, the simplified form of this expression would be x10. Using that same logic, given (91/2)2, to simplify the exponents would be multiplied together: 91/2*2= 91= 9. Now thinking in reverse....if asked to find 2 identical numbers that could be multiplied together to get 9, we would most likely say 3, because we know 3 * 3 (or 32) = 9. If both (91/2)2 and 32= 9, then 91/2 must equal 3. For that to be true 91/2must be9. It is now understandable that, 9* 9= 3 * 3 = 9. We can summarize this logic in the following general equation:1nna=a, which can then be expanded to:()mmnmnnaaa==. The first equation shows the numerator of the rational exponent as one, but we know that is not always the case, i.e., 3/4, 7/8, so the second rule is a more general rule that shows when we convert the expression from its exponential expression form to its radical expression form the denominator of the rational