Giải Bài 1 trang 13 SGK Toán 11 Chân trời sáng tạo tập 2 - CTST

Lời giải chi tiết

a) \({\left( {\frac{3}{4}} \right)^{ - 2}}{.3^2}{.12^0} \)\(= \frac{1}{{{{\left( {\frac{3}{4}} \right)}^2}}}{.3^2}.1 \)\(= \frac{1}{{\frac{9}{{16}}}}.9\)\( = \frac{{16}}{9}.9 = 16\).

b) \({\left( {\frac{1}{{12}}} \right)^{ - 1}}.{\left( {\frac{2}{3}} \right)^{ - 2}} \)\(= \frac{1}{{\frac{1}{{12}}}}.\frac{1}{{{{\left( {\frac{2}{3}} \right)}^2}}} \)\(= 12.\frac{1}{{\frac{4}{9}}} \)\(= 12.\frac{9}{4} = 27\).

c) \({\left( {{2^{ - 2}}{{.5}^2}} \right)^{ - 2}}:\left( {{{5.5}^{ - 5}}} \right) \)\(= {\left( {\frac{{{5^2}}}{{{2^2}}}} \right)^{ - 2}}:\left( {{5^{1 + \left( { - 5} \right)}}} \right) \)\(= \frac{1}{{{{\left( {\frac{{{5^2}}}{{{2^2}}}} \right)}^2}}}:{5^{ - 4}}\)\( = \frac{1}{{\frac{{{5^4}}}{{{2^4}}}}}:\frac{1}{{{5^4}}}\)\( = \frac{{{2^4}}}{{{5^4}}}{.5^4} \)\(= {2^4} = 16\).

-- Mod Toán 11 HỌC247