My Math Forum Why is choice 3 the answer?

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 January 29th, 2018, 10:02 PM #1 Senior Member   Joined: Apr 2008 Posts: 193 Thanks: 3 Why is choice 3 the answer? (ex) Which of the following statements is true? (1) If P=Q, then P^n=Q^n where n is any integer (2) If P^n=Q^n, then P=Q where n is any integer (3) If P=Q, then P^n=Q^n where n is any positive integer (4) If P^n=Q^n, then P=Q where n is any positive integer my attempt If I let P and Q be 2 and let n be 1, these values satisfy all four choices. Next, I let P and Q be 2 and let n be -1. these values satisfy (1) and (2). So, I don't know why the answer key says (3) is the answer. Please help me. Thanks a lot.
 January 29th, 2018, 10:58 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,122 Thanks: 1102 you can't prove anything by finding an example that works, you can only disprove something by finding an example that doesn't. (1) would be true except that 1/0 is undefined so that the statement isn't true when P=Q=0 when n is negative (2) isn't true for Q=-P and n even (3) is true (4) is false for the same reason as (2) Thanks from davedave
 January 30th, 2018, 10:49 PM #3 Senior Member   Joined: Apr 2008 Posts: 193 Thanks: 3 Thank you very much again, romsek.

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