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

Question

Chloe Noble

SAT

17 March, 21:58

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

+4

Answers (1)

Know the Answer?

Desmond Andrews · 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.