Which of the following is always true? a) if p=q then p^n=q^n, n an integer b) if p^n=q^n then p=q, n an integer c) if p=q then p^n = q^n, n a positive integer d) if p^n=q^n then p=q, n a positive integer

Answer is  c) if p=q then p^n = q^n, n a positive integer======we can find counterexamples  to disprove the fact that something is true for all cases.the following choice    a) if p=q then p^n=q^n, n an integerhave  as any integer.integers are numbers belonging to the set    there are no restrictions on  and  .if  , and n is a negative exponent, then, by the exponent property  , raising 0 to a negative power results in a division by zero.so choice (a) is not always true.(also, there's the whole debate about  ,  ,  , then the condition of    is true because squaring a negative number (negative times a negative) makes a positive. but the values of  and  themselves are not equal.choices (b) and (d) are not always true.by process of elimination, choice (c) is the answer.we can also reason that  if two numbers are the same, then raising them to a positive integer exponent (positive means not including 0) will still be the same thing. positive integer exponents implies repeated multiplication.

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