Solved: Suppose that in standard factored form a = pe1 1 pe2 2 pek k , where k is a

Chapter 4, Problem 39

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Suppose that in standard factored form a = pe1 1 pe2 2 pek k , where k is a positive integer; p1, p2,..., pk are prime numbers; and e1, e2,..., ek are positive integers. a. What is the standard factored form for a3? b. Find the least positive integer k such that 24 35 7112 k is a perfect cube (i.e., equals an integer to the third power). Write the resulting product as a perfect cube.

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