Thực hiện phép tính
\(a)\dfrac{{{5^4}{{.20}^4}}}{{{{25}^5}{{.4}^5}}}\)
\(b)\dfrac{{{4^3}{{.25}^5}{{.9}^3}}}{{{8^2}{{.125}^3}{{.3}^5}}}\)
\(c)\dfrac{{{6^3} + {{3.6}^2} + {3^3}}}{{ - 13}}\)
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\(a)\dfrac{{{5^4}{{.20}^4}}}{{{{25}^5}{{.4}^5}}} = \dfrac{{{5^4}.{{(5.4)}^4}}}{{{{({5^2})}^5}{{.4}^5}}} = \dfrac{{{5^4}{{.5}^4}{{.4}^4}}}{{{5^{10}}{{.4}^5}}} = \dfrac{{{5^8}{{.4}^4}}}{{{5^{10}}{{.4}^5}}} = \dfrac{1}{{{5^2}.4}} = \dfrac{1}{{100}}\)
\(b)\dfrac{{{4^3}{{.25}^5}{{.9}^3}}}{{{8^2}{{.125}^3}{{.3}^5}}} = \dfrac{{{{({2^2})}^3}.{{({5^2})}^5}.{{({3^2})}^3}}}{{{{({2^3})}^2}.{{({5^3})}^3}{{.3}^5}}} = \dfrac{{{2^6}{{.5}^{10}}{{.3}^6}}}{{{2^6}{{.5}^9}{{.3}^5}}} = 5.3 = 15\)
\(\begin{array}{l}c)\dfrac{{{6^3} + {{3.6}^2} + {3^3}}}{{ - 13}} = \dfrac{{{{(2.3)}^3} + 3.{{(3.2)}^2} + {3^3}}}{{ - 13}} = \dfrac{{{2^3}{{.3}^3} + {{3.3}^2}{{.2}^2} + {3^3}}}{{ - 13}}\\ = \dfrac{{{2^3}{{.3}^3} + {3^3}{{.2}^2} + {3^3}}}{{ - 13}} = \dfrac{{{3^3}.({2^3} + {2^2} + 1)}}{{ - 13}} = \dfrac{{{{13.3}^3}}}{{ - 13}} = - {3^3} = - 27\end{array}\)