If 2x × 3y × 5z = 2160,


If $2^{x} \times 3^{y} \times 5^{y}=2160$, find $x, y$ and $z$. Hence compute the value of $3^{x} \times 2^{-y} \times 5^{-z}$


$2^{x} \times 3^{y} \times 5^{z}=2160$

$2^{x} \times 3^{y} \times 5^{z}=2^{4} \times 3^{3} \times 5^{1}$

$x=4, y=3, z=1$

$3^{x} \times 2^{-y} \times 5^{-z}=3^{4} \times 2^{-3} \times 5^{-1}$

$=\frac{3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 5}$

$=81 / 40$

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