Question

$If{2}^x\times 3^y\times 5^z=2160,findx,yandz.Hence,computethevalueof{3}^x\times 2^{-y}\times 5^{-z}.$

Answer 1

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

$2^x\times 3^y\times 5^z=2^4\times 3^3\times 5^{1}Comparing,wegetx=4,y=3,z=1Now,3^x\times 2^{-y}\times 5^{-z}=3^4\times 2^{-3}\times 5^{-1}=\frac{81}{8\times 5}=\frac{81}{40}$