Bài 1: Tính nhanh: \(D = {2009^{\left( {1000 – {1^3}} \right)\left( {1000 – {2^3}} \right)…\left( {1000 – {{15}^3}} \right)}}\)
Bài 2: Tính nhanh giá trị biểu thức: \(A = {{{{14}^{16}}{{.21}^{32}}{{.35}^{48}}} \over {{{10}^{16}}{{.15}^{32}}{{.7}^{96}}}}\)
Bài 3: Tìm \(x \in\mathbb Z\) biết:
a) \({\left( {2x – 3} \right)^2} = 25\)
b) \({{27} \over {{3^x}}} = 3.\)
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Bài 1: \(D = {2009^0} = 1\)
Bài 2: \(\eqalign{A &= {{{{14}^{16}}{{.21}^{32}}{{.35}^{48}}} \over {{{10}^{16}}{{.15}^{32}}{{.7}^{96}}}}\cr& = {{{{\left( {2.7} \right)}^{16}}.{{\left( {3.7} \right)}^{32}}.{{\left( {5.7} \right)}^{48}}} \over {{{\left( {2.5} \right)}^{16}}.{{\left( {3.5} \right)}^{32}}{{.7}^{96}}}}\cr& = {{{2^{16}}{{.7}^{16}}{{.3}^{32}}{{.7}^{32}}{{.5}^{48}}{{.7}^{48}}} \over {{2^{16}}{{.5}^{16}}{{.3}^{32}}{{.5}^{32}}{{.7}^{96}}}} \cr&= {{{2^{16}}{{.5}^{48}}{{.7}^{96}}} \over {{2^{16}}{{.5}^{48}}{{.7}^{96}}}} = 1\cr}\)
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Bài 3: a) \({\left( {2x – 3} \right)^2} = 25\)
\(\Rightarrow 2x – 3 = 5\) hoặc \(2x – 3 = – 5\)
\( \Rightarrow 2x = 8\) hoặc \(2x = – 2\)
\( \Rightarrow x = 4\) hoặc \(x = – 1.\)
b) \({{27} \over {{3^x}}} = 3 \Rightarrow {3^x} = 27:3\)
\(\Rightarrow {3^x} = 9 \Rightarrow {3^x} = {3^2} \)
\(\Rightarrow x = 2.\)
