Simplify (2/3)^3 (1/5 x 2/3)^-3 (1/5)^4
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Answer:
[tex](\frac{2}{3})^{3} (\frac{1}{5}.\frac{2}{3} )^{-3} (\frac{1}{5})^{4} =(\frac{2^{3} }{3^{3} }) (\frac{2}{8} )^{-3} (\frac{1^{4}} {5^{4} })[/tex]
[tex]=(\frac{2^{3} }{3^{3} }) (\frac{2^{-3} }{8^{-3} } ) (\frac{1^{4}} {5^{4} })[/tex]
[tex]=\frac{2^{3} .2^{-3}.8^{3}. 1 }{3^{3} .5^{4} }[/tex]
[tex]=\frac{1.8^{3} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{(2^{3}) ^{3} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{2^{9} }{3^{3} .5^{4} }[/tex]
[tex]=\frac{512}{27.625}[/tex]
[tex]=\frac{512}{16875}[/tex]