Blue book math question

Test Preparation
1

<p>pg.790 </p>

<p>19.) If k,n,x, and y are positive numbers satisfying x^-4/3=k^-2 and y^4/3=n^2, what is (xy)^-2/3 in terms of n and k?
A.) 1/nk
B.) n/k
C.) k/n
D.) nk
E.) 1
The answer is A and idk how they got to that answer so can someone explain?</p>

2

<p>(x^-4/3)^(1/2) = x^-2/3, and (k^-2)^(1/2)=k^-1
(y^4/3)^(-1/2) = y^-2/3, and (n^2)^(-1/2)=n^-1</p>

<p>(x^-2/3 *y^-2/3) = (xy)^-2/3 = (nk)^-1 = 1/nk</p>

<p>QED</p>