assuming you mean something like
[tex](\frac{3}{4})(\frac{8}{9})(\frac{15}{16})(\frac{24}{25})(\frac{35}{36})(\frac{48}{49})(\frac{63}{64})(\frac{80}{81})(\frac{99}{100})[/tex]
so
remember [tex](\frac{a}{b})(\frac{c}{d})=\frac{ac}{bd}[/tex]
so
[tex](\frac{3}{4})(\frac{8}{9})(\frac{15}{16})(\frac{24}{25})(\frac{35}{36})(\frac{48}{49})(\frac{63}{64})(\frac{80}{81})(\frac{99}{100})=[/tex]
[tex]\frac{(3)(8)(15)(24)(35)(48)(63)(80)(99)}{(4)(9)(16)(25)(36)(49)(64)(81)(100)}[/tex]
factor out some things
[tex]\frac{(3)(2^3)(3)(5)(2^3)(3)(5)(7)(2^4)(3)(3^2)(7)(2^4)(5)(3^2)(11)}{(2^2)(3^2)(2^4)(5^2)(2^2)(3^2)(7^2)(2^6)(3^4)(2^2)(5^2)}=[/tex]
[tex]\frac{(2^{14})(3^8)(5^3)(7^2)(11)}{(2^{16})(3^8)(5^4)(7^2)}=[/tex]
[tex]\frac{11}{(2^2)(5^1)}=\frac{11}{20}[/tex]
