If x is a positive integer such than x⁹=r and x⁵=w, which of the following must be equal to x^13

Question

SAT

Arjun Franco

9 May, 18:57

If x is a positive integer such than x⁹=r and x⁵=w, which of the following must be equal to x^13

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Answers (1)

Know the Answer?

Joel Ayers · Answer 1

The answer is (r^2) / w.

Explanation:

Notice that 9 + 9 - 5 = 18 - 5 = 13. Therefore, we want to be able to express x^ (9 + 9 - 5), which is the same as x^9 * x^9 * x^ (-5). We know x^9 = r, and x^ (-5) is just 1 / (x^5) = 1/w. Therefore, our answer is r*r*1/w = (r^2) / w.