# Math Help - Exponents

1. ## Exponents

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?

2. Originally Posted by Alan306090
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?
$x^{-\frac{4}{3}} = k^{-2}$

$\left(x^{-\frac{2}{3}}\right)^2 = k^{-2}$

$x^{-\frac{2}{3}} = k^{-1}$.

$y^{\frac{4}{3}} = n^2$

$y^{-\frac{4}{3}} = n^{-2}$

Now use a similar process to find $y^{-\frac{2}{3}}$.

Then remember that $(xy)^{-\frac{2}{3}} = x^{-\frac{2}{3}}y^{-\frac{2}{3}}$.