EXPLAIN HOW THE DEFINITION OF THE MEANING OF RATIONAL EXPONENTS FOLLOWS FROM EXTENDING THE PROPERTIES OF INTEGER EXPONENTS TO THOSE VALUES, ALLOWING FOR A NOTATION FOR RADICALS IN TERMS OF RATIONAL EXPONENTS. FOR EXAMPLE, WE DEFINE 5^(1/3) TO BE THE CUBE ROOT OF 5 BECAUSE WE WANT [5^(1/3)]^3 = 5^(1/3)3 TO HOLD, SO [5^(1/3)]^3 MUST EQUAL 5.
REWRITE EXPRESSIONS INVOLVING RADICALS AND RATIONAL EXPONENTS USING THE PROPERTIES OF EXPONENTS.
EXPLAIN WHY: THE SUM OR PRODUCT OF TWO RATIONAL NUMBERS IS RATIONAL; THE SUM OF A RATIONAL NUMBER AND AN IRRATIONAL NUMBER IS IRRATIONAL; AND THE PRODUCT OF A NONZERO RATIONAL NUMBER AND AN IRRATIONAL NUMBER IS IRRATIONAL.
Mississippi: N-RN Math Standards