Thực hiện phép tính:
a) \(\dfrac{{13}}{{50}}.\left( { - 15,5} \right) - \dfrac{{13}}{{50}}.84\dfrac{1}{2}\)
b) \(\dfrac{2}{9} + \dfrac{1}{3}:\left( { - \dfrac{3}{2}} \right) + \dfrac{1}{2}.\left( { - 0,5} \right)\)
c) \(4.{\left( { - \dfrac{1}{2}} \right)^3} - 2.{\left( {\dfrac{{ - 1}}{2}} \right)^2} + 3.\left( { - \dfrac{1}{2}} \right) + 1\)
d) \(\dfrac{{{{\left( { - 0,7} \right)}^2}.{{\left( { - 5} \right)}^3}}}{{{{\left( {\dfrac{{ - 7}}{3}} \right)}^3}.{{\left( {\dfrac{3}{2}} \right)}^4}.{{\left( { - 1} \right)}^5}}}\)
a) \(\dfrac{{13}}{{50}}.\left( { - 15,5} \right) - \dfrac{{13}}{{50}}.84\dfrac{1}{2}\)
b) \(\dfrac{2}{9} + \dfrac{1}{3}:\left( { - \dfrac{3}{2}} \right) + \dfrac{1}{2}.\left( { - 0,5} \right)\)
c) \(4.{\left( { - \dfrac{1}{2}} \right)^3} - 2.{\left( {\dfrac{{ - 1}}{2}} \right)^2} + 3.\left( { - \dfrac{1}{2}} \right) + 1\)
d) \(\dfrac{{{{\left( { - 0,7} \right)}^2}.{{\left( { - 5} \right)}^3}}}{{{{\left( {\dfrac{{ - 7}}{3}} \right)}^3}.{{\left( {\dfrac{3}{2}} \right)}^4}.{{\left( { - 1} \right)}^5}}}\)
a), b) Thực hiện phép cộng, trừ nhân chia số hữu tỉ.
c), d) Thực hiện phép tính có lũy thừa của một số hữu tỉ.
Chú ý: \({\left( {\dfrac{x}{y}} \right)^n} = \dfrac{{{x^n}}}{{{y^n}}}\left( {y \ne 0} \right)\)
\(\dfrac{{{x^m}}}{{{x^n}}} = {x^m}:{x^n} = {x^{m - n}}\)\(\left( {x \ne 0;m,n \in {\mathbb{N}^*}} \right)\)
a) \(\dfrac{{13}}{{50}}.\left( { - 15,5} \right) - \dfrac{{13}}{{50}}.84\dfrac{1}{2}\)
\(\begin{array}{l} = \dfrac{{13}}{{50}}.\left( { - 15,5 - 84\dfrac{1}{2}} \right)\\ = \dfrac{{13}}{{50}}.\left( {\dfrac{{ - 31}}{2} - \dfrac{{169}}{2}} \right)\\ = \dfrac{{13}}{{50}}.\dfrac{{\left( { - 200} \right)}}{2}\\ = - 26\end{array}\)
b) \(\dfrac{2}{9} + \dfrac{1}{3}:\left( { - \dfrac{3}{2}} \right) + \dfrac{1}{2}.\left( { - 0,5} \right)\)
\(\begin{array}{l} = \dfrac{2}{9} + \dfrac{1}{3}.\left( { - \dfrac{2}{3}} \right) + \dfrac{1}{2}.\left( {\dfrac{{ - 1}}{2}} \right)\\ = \dfrac{2}{9} + \dfrac{{ - 2}}{9} + \dfrac{{ - 1}}{4}\\ = \left( {\dfrac{2}{9} + \dfrac{{ - 2}}{9}} \right) + \dfrac{{ - 1}}{4}\\ = 0 + \dfrac{{ - 1}}{4}\\ = \dfrac{{ - 1}}{4}\end{array}\)
c) \(4.{\left( { - \dfrac{1}{2}} \right)^3} - 2.{\left( {\dfrac{{ - 1}}{2}} \right)^2} + 3.\left( { - \dfrac{1}{2}} \right) + 1\)
\(\begin{array}{l} = 4.\dfrac{{{{\left( { - 1} \right)}^3}}}{{{2^3}}} - 2.\dfrac{{{{\left( { - 1} \right)}^2}}}{{{2^2}}} + \dfrac{{ - 3}}{2} + 1\\ = 4.\dfrac{{ - 1}}{8} - 2.\dfrac{1}{4} + \dfrac{{ - 3}}{2} + 1\\ = \dfrac{{ - 1}}{2} - \dfrac{1}{2} + \dfrac{{ - 3}}{2} + \dfrac{2}{2}\\ = \dfrac{{ - 1 - 1 + \left( { - 3} \right) + 2}}{2}\\ = \dfrac{{ - 3}}{2}\end{array}\)
d) \(\dfrac{{{{\left( { - 0,7} \right)}^2}.{{\left( { - 5} \right)}^3}}}{{{{\left( {\dfrac{{ - 7}}{3}} \right)}^3}.{{\left( {\dfrac{3}{2}} \right)}^4}.{{\left( { - 1} \right)}^5}}}\)
\(\begin{array}{l} = \dfrac{{{{\left( {\dfrac{{ - 7}}{{10}}} \right)}^2}.{{\left( { - 5} \right)}^3}}}{{\dfrac{{{{\left( { - 7} \right)}^3}}}{{{3^3}}}.\dfrac{{{3^4}}}{{{2^4}}}.\left( { - 1} \right)}} = \dfrac{{\dfrac{{{{\left( { - 7} \right)}^2}}}{{{{\left( {2.5} \right)}^2}}}.{{\left( { - 1.5} \right)}^3}}}{{{{\left( { - 7} \right)}^3}.\dfrac{3}{{{2^4}}}.\left( { - 1} \right)}}\\ = \dfrac{{\dfrac{{{{\left( { - 7} \right)}^2}.{{\left( { - 1} \right)}^3}{{.5}^3}}}{{{2^2}{{.5}^2}}}}}{{\dfrac{{{{\left( { - 7} \right)}^3}.3.\left( { - 1} \right)}}{{{2^4}}}}} = \dfrac{{{{\left( { - 7} \right)}^2}.{{\left( { - 1} \right)}^3}{{.5}^3}}}{{{2^2}{{.5}^2}}}:\dfrac{{{{\left( { - 7} \right)}^3}.3.\left( { - 1} \right)}}{{{2^4}}}\\ = \dfrac{{{{\left( { - 7} \right)}^2}.{{\left( { - 1} \right)}^3}{{.5}^3}}}{{{2^2}{{.5}^2}}}.\dfrac{{{2^4}}}{{{{\left( { - 7} \right)}^3}.3.\left( { - 1} \right)}}\\ = \dfrac{1}{{\left( { - 7} \right)}}.\dfrac{{{{\left( { - 1} \right)}^2}}}{1}.\dfrac{5}{1}.\dfrac{{{2^2}}}{1}.\dfrac{1}{3}\\ = \dfrac{{5.4}}{{\left( { - 7} \right).3}} = \dfrac{{20}}{{ - 21}} = \dfrac{{ - 20}}{{21}}\end{array}\)
