<p>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?</p>
<p>A. 1/nk
B. n/k
c. k/n
d. nk
e. 1
the answer is:A</p>
<p>(x · y)^(-2/3)</p>
<p>[(x · y)^(-4/3)]^(1/2) <---- Rule of exponents</p>
<p>[x^(-4/3)]^(1/2) · [y^(-4/3)]^(1/2) <—Rule of exponents</p>
<p>[x^(-4/3)]^(1/2) · [1/(y^(4/3))]^(1/2) <—Rule of exponents</p>
<p>[k^(-2)]^(1/2) · [1/(n^2)]^(1/2) <—Subsitute</p>
<p>[k^(-1)] · [1/n] <—Simplify</p>
<p>[1/k] · [1/n] <—Rule of exponents</p>
<p>1/(kn) <—Multiply</p>
<p>I didn’t have to separate them out then combine them back, it just looked a bit cleaner if I did that here. It looks pretty messy like this anyhow, so hopefully that helps.</p>