Tìm giá trị của biểu thức sau
a) \(\frac{4^{2}.4^{3}}{2^{10}}\)
b) \(\frac{(0,6)^{5}}{(0,2)^{6}}\)
c)\(\frac{2^{7}. 9^{3}}{6^{5}.8^{2}}\)
d) \(\frac{6^{3} + 3.6^{2}+ 3^{3}}{-13}\)
Chú ý các công thức sau:
\(\begin{array}{l}
{\left( {x.y} \right)^n} = {x^n}.{y^n}\\
{\left( {\frac{x}{y}} \right)^n} = \frac{{{x^n}}}{{{y^n}}}\,\,\left( {y \ne 0} \right)
\end{array}\)
\({\left( {{x^n}} \right)^m} = {x^{n.m}}\)
Lời giải chi tiết
a) \(\frac{4^{2}.4^{3}}{2^{10}}\) = \(\frac{4^{5}}{(2^{2})^{5}}=\frac{4^{5}}{4^{5}}= 1\)
b) \(\frac{(0,6)^{5}}{(0,2)^{6}}\) = \(\frac{(0,2.3)^{5}}{(0,2)^{6}} = \frac{(0,2)^{5}.3^{5}}{(0,2)^{5}.0,2} = \frac{3^{5}}{0,2} = \frac{243}{0,2}= 1215\)
c)
\(\frac{{{2^7}{{.9}^3}}}{{{6^5}{{.8}^2}}} = \frac{{{2^7}.{{\left( {{3^2}} \right)}^3}}}{{{{\left( {2.3} \right)}^5}.{{\left( {{2^3}} \right)}^2}}} = \frac{{{2^7}{{.3}^6}}}{{{2^5}{{.3}^5}{{.2}^6}}} = \frac{{{2^7}{{.3}^6}}}{{{2^{11}}{{.3}^5}}}\)\( = \frac{3}{{{2^4}}} = \frac{3}{{16}}\)
(Áp dụng công thức: \({\left( {{x^n}} \right)^m} = {x^{n.m}};\,\,{\left( {x.y} \right)^n} = {x^n}.{y^n}\))
d) \(\frac{6^{3} + 3.6^{2}+ 3^{3}}{-13}= {{{{\left( {2.3} \right)}^3} + 3.{{\left( {2.3} \right)}^2} + {3^3}} \over { - 13}}\)\(=\frac{2^{3}.3^{3} + 3^{3}.2^{2} + 3^{3}}{-13} = \frac{3^{3}.(2^{3} + 2^{2} + 1)}{-13}\)\(= -3^{3} = -27\)
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