Question:
If $2^{x} \times 3^{y} \times 5^{y}=2160$, find $x, y$ and $z$. Hence compute the value of $3^{x} \times 2^{-y} \times 5^{-z}$
Solution:
$2^{x} \times 3^{y} \times 5^{z}=2160$
$2^{x} \times 3^{y} \times 5^{z}=2^{4} \times 3^{3} \times 5^{1}$
$x=4, y=3, z=1$
$3^{x} \times 2^{-y} \times 5^{-z}=3^{4} \times 2^{-3} \times 5^{-1}$
$=\frac{3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 5}$
$=81 / 40$