[tex]1. \\ a) \: ( \frac{2}{3} ) {}^{5} = \frac{2 {}^{5} }{3 {}^{5} } = \frac{32}{243} \\ b) \: ( \frac{11}{14} ) {}^{0} = 1 \\ c) \: ( \frac{1}{9} ) {}^{3} = \frac{1}{9 {}^{3} } = \frac{1}{729} \\ d) \: ( \frac{23}{99} ) {}^{2} = \frac{23 {}^{2} }{99 {}^{2} } = \frac{529}{9801} \\ e) \: (2 \frac{1}{4} ) {}^{3} = ( \frac{9}{4} ) {}^{3} = \frac{9 {}^{3} }{4 {}^{3} } = \frac{729}{64} [/tex]
[tex]3. \\ a) \: ( \frac{5}{4} ) {}^{7} \div ( \frac{5}{4}) {}^{4} = ( \frac{5}{4} ) {}^{3} = \frac{5 {}^{3} }{4 {}^{3} } = \frac{125}{64} \\ b) \: ( \frac{21}{13} ) {}^{52} \div ( \frac{21}{13} ) {}^{51} = \frac{21}{13} \\ c) \: (4 \frac{1}{4} ) {}^{12} \div (4 \frac{1}{4} ) {}^{10} = (4 \frac{1}{4} ) {}^{2} = \frac{9 {}^{2} }{4 {}^{2} } = \frac{81}{16} \\ d) \: ( \frac{49}{9} ) {}^{18} \div (5 \frac{4}{9} ) {}^{17} = ( \frac{49}{9} ) {}^{18} \div ( \frac{49}{9} ) {}^{17} = \frac{49}{9} \\ e) \: (1 \frac{1}{2} ) {}^{15} \div ( \frac{3}{2} ) {}^{11} = ( \frac{3}{2} ) {}^{15} \div ( \frac{3}{2} ) {}^{11} = ( \frac{3}{2} ) {}^{4} = \frac{3 {}^{4} }{2 {}^{4} } = \frac{81}{16} \\ f) \: (4 \frac{4}{15} ) {}^{23} \div ( \frac{64}{15} ) {}^{22} = ( \frac{64}{15} ){}^{23} \div ( \frac{64}{15} ) {}^{22} = \frac{64}{15} [/tex]
