Carcass wrote:

\(a^3b^4c^7>0\)

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Key Concept:

(any number)^(EVEN INTEGER) ≥ 0 First, since \(a^3b^4c^7>0\), we know that a ≠ 0, b ≠ 0, and c ≠ 0

Next, since \(b^4\) must be POSITIVE, we can safely divide both sides of the inequality by \(b^4\) to get: \(a^3c^7>0\)

Also, since \(c^6\) must be POSITIVE, we can safely divide both sides of the inequality by \(c^6\) to get: \(a^3c>0\)

Finally, since \(a^2\) must be POSITIVE, we can safely divide both sides of the inequality by \(a^2\) to get: \(ac>0\)

So, the ONLY relevant conclusion we can make is that \(ac>0\)

Answer: C

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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