So sánh:
a)\(\left(0,5\right)^6\)và \(\left(0,5\right)^9\)
b)\(\left(-0,125\right)^8\)và \(\left(0,5\right)^{24}\)
c)\(8^{12}\) và \(12^8\)
So sánh:
a) \(3^6\)và\(6^3\)
b) \(\left(0,5\right)^6\)và \(\left(0,5\right)9\)
c)\(\left(-0,125\right)^8\)và \(\left(0,5\right)^{24}\)
d)\(8^{12}\)và \(12^8\)
a) 63
36 = 32.3 = ( 32)3 = 93
Do 6 < 9 nên 63 < 93 hay 63 < 36
^^
a) 63 = 63
36 =( 32)3 = 93
Vì 9 > 6 nên 93 > 63 hay 36 > 63
So sánh:
a) \({( - 2)^4} \cdot {( - 2)^5}\) và \({( - 2)^{12}}:{( - 2)^3}\);
b) \({\left( {\frac{1}{2}} \right)^2} \cdot {\left( {\frac{1}{2}} \right)^6}\) và \({\left[ {{{\left( {\frac{1}{2}} \right)}^4}} \right]^2}\)
c) \({(0,3)^8}:{(0,3)^2}\) và \({\left[ {{{(0,3)}^2}} \right]^3}\);
d) \({\left( { - \frac{3}{2}} \right)^5}:{\left( { - \frac{3}{2}} \right)^3}\) và \({\left( {\frac{3}{2}} \right)^2}\).
a) \({( - 2)^4} \cdot {( - 2)^5} = {\left( { - 2} \right)^{4 + 5}} = {\left( { - 2} \right)^9}\)
\({( - 2)^{12}}:{( - 2)^3} = {\left( { - 2} \right)^{12 - 3}} = {\left( { - 2} \right)^9}\)
Vậy \({( - 2)^4} \cdot {( - 2)^5}\) = \({( - 2)^{12}}:{( - 2)^3}\);
b) \({\left( {\frac{1}{2}} \right)^2} \cdot {\left( {\frac{1}{2}} \right)^6} = {\left( {\frac{1}{2}} \right)^{2 + 6}} = {\left( {\frac{1}{2}} \right)^8}\)
\({\left[ {{{\left( {\frac{1}{2}} \right)}^4}} \right]^2} = {\left( {\frac{1}{2}} \right)^{4.2}} = {\left( {\frac{1}{2}} \right)^8}\)
Vậy \({\left( {\frac{1}{2}} \right)^2} \cdot {\left( {\frac{1}{2}} \right)^6}\) = \({\left[ {{{\left( {\frac{1}{2}} \right)}^4}} \right]^2}\)
c) \({(0,3)^8}:{(0,3)^2} = {\left( {0,3} \right)^{8 - 2}} = {\left( {0,3} \right)^6}\)
\({\left[ {{{(0,3)}^2}} \right]^3} = {\left( {0,3} \right)^{2.3}} = {\left( {0,3} \right)^6}\)
Vậy \({(0,3)^8}:{(0,3)^2}\)= \({\left[ {{{(0,3)}^2}} \right]^3}\).
d) \({\left( { - \frac{3}{2}} \right)^5}:{\left( { - \frac{3}{2}} \right)^3} = {\left( { - \frac{3}{2}} \right)^{5 - 3}} = {\left( { - \frac{3}{2}} \right)^2} = {\left( {\frac{3}{2}} \right)^2}\)
Vậy \({\left( { - \frac{3}{2}} \right)^5}:{\left( { - \frac{3}{2}} \right)^3}\) = \({\left( {\frac{3}{2}} \right)^2}\).
(-2) ^4 . (-2) 65 và ( -2) ^ 12 : ( -2) ^3
=( -2) ^ 4+5 =(-2)^9 và (-2) ^12-3 = ( -2) ^9
vậy ( -2) ^9 = (-2) ^9
Nên (-2) ^4 .( -2) ^5 = ( -2) ^ 12 : ( -2) ^3
Tính
a) \(\left( {\frac{4}{5} - 1} \right):\frac{3}{5} - \frac{2}{3}.0,5\)
b) \(1 - {\left( {\frac{5}{9} - \frac{2}{3}} \right)^2}:\frac{4}{{27}}\)
c)\(\left[ {\left( {\frac{3}{8} - \frac{5}{{12}}} \right).6 + \frac{1}{3}} \right].4\)
d) \(0,8:\left\{ {0,2 - 7.\left[ {\frac{1}{6} + \left( {\frac{5}{{21}} - \frac{5}{{14}}} \right)} \right]} \right\}\)
a)
\(\begin{array}{l}\frac{1}{9} - 0,3.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{10}}.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{2.5}}.\frac{5}{{3.3}} + \frac{1}{3}\\ = \frac{1}{9} - \frac{1}{6} + \frac{1}{3}\\ = \frac{2}{{18}} - \frac{3}{{18}} + \frac{6}{{18}}\\ = \frac{5}{{18}}\end{array}\)
b)
\(\begin{array}{l}{\left( {\frac{{ - 2}}{3}} \right)^2} + \frac{1}{6} - {\left( { - 0,5} \right)^3}\\ = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{2}} \right)^3\\ = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{8}} \right)\\ = \frac{4}{9} + \frac{1}{6} + \frac{1}{8}\\ = \frac{{32}}{{72}} + \frac{{12}}{{72}} + \frac{9}{{72}}\\ = \frac{{53}}{{72}}\end{array}\)
Viết các số \({\left( {0,25} \right)^8};\,\,{\left( {0,125} \right)^4};{\left( {0,0625} \right)^2}\)dưới dạng lũy thừa cơ số 0,5.
\(\begin{array}{l}{\left( {0,25} \right)^8} = {\left[ {{{\left( {0,5} \right)}^2}} \right]^8}=(0,5)^{2.8} = {\left( {0,5} \right)^{16}};\\{\left( {0,125} \right)^4} = {\left[ {{{\left( {0,5} \right)}^3}} \right]^4} =(0,5)^{3.4}= {\left( {0,5} \right)^{12}};\\{\left( {0,0625} \right)^2} = {\left[ {{{\left( {0,5} \right)}^4}} \right]^2} =(0,5)^{4.2}= {\left( {0,5} \right)^8}\end{array}\)
Tính:
a)\(\left\{\left[\left(6,2:0,31-\frac{5}{6}.0,9\right).0,2+0,15\right]:0,2\right\}:\left[\left(2+1\frac{4}{11}:0,1\right).\frac{1}{33}\right]\)
b)\(0,4\left(3\right)+0,6\left(2\right)-2\frac{1}{2}.\left[\left(\frac{1}{2}+\frac{1}{3}:0,5\left(8\right)\right)\right]:\frac{50}{53}\)
c)\(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}\)
c) \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}=\frac{3\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}{5\left(0,123-0,1+\frac{1}{11}+\frac{1}{12}\right)}=\frac{3}{5}\)
So sánh:
a/\(3^{12}\) và \(5^8\) c/\(\left(0,6\right)^9\)và \(\left(-0,9\right)^6\)
b/\(8^{12}\)và \(12^8\) d/\(\left(0,3\right)^{100}\)và \(\left(0,5\right)^{201}\)
a/ 312 và 58
312=(33)4=274 58=(52)4=254
vậy 312 > 58
b. \(\dfrac{8^2.6^3}{9^2.16^2}\)
c. \(\dfrac{\left(0,15\right)^4}{\left(0,5\right)^5}\)
d. \(\left(\dfrac{3}{4}\right)^3\). \(\left(\dfrac{16}{9}\right)^3\)
\(\dfrac{8^2.6^3}{9^2.16^2}=\dfrac{\left(2^3\right)^2.2^3.3^3}{\left(3^2\right)^2.\left(2^4\right)^2}=\dfrac{2^{3.2+3}.3^3}{3^4.2^8}=\dfrac{3^3.2^8.2}{3.3^3.2^8}=\dfrac{2}{3}\\ ---\\ \dfrac{\left(0,15\right)^4}{\left(0,5\right)^5}=\left(\dfrac{0,15}{0,5}\right)^4.\dfrac{1}{0,5}=\left(\dfrac{3}{10}\right)^4.2=\dfrac{81}{10000}.2=\dfrac{81}{5000}\\ ---\\ d,\left(\dfrac{3}{4}\right)^3.\left(\dfrac{16}{9}\right)^3=\left(\dfrac{3}{4}.\dfrac{16}{9}\right)^3=\left(\dfrac{48}{32}\right)^3=\left(\dfrac{3}{2}\right)^3=\dfrac{27}{8}\)
b) \(\dfrac{8^2.6^3}{9^2.16^2}=\dfrac{2^6.2^3.3^3}{3^4.2^8}=\dfrac{2^9.3^3}{3^4.2^8}=\dfrac{2}{3}\)
c) \(\dfrac{\left(0,15\right)^4}{\left(0,5\right)^5}=\dfrac{\left(0,5\right)^4.\left(0,3\right)^4}{\left(0,5\right)^5}=\dfrac{0,3^4}{0,5}\)
d) \(\left(\dfrac{3}{4}\right)^3.\left(\dfrac{16}{9}\right)^3=\dfrac{3^3}{4^3}.\dfrac{4^6}{3^6}=\dfrac{4^3}{3^3}=\left(\dfrac{4}{3}\right)^3\)
b. \(\dfrac{2}{3}\)
c. \(\dfrac{81}{5000}\)
d. \(\dfrac{64}{27}\)
\(A=\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{-0,625+0,5-\frac{5}{11}-\frac{5}{12}}+\frac{1,5+1-0,75}{2,5+\frac{5}{3}-1,25}\)
\(A=\frac{3\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}{-5\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}+\frac{3\left(0,5+\frac{1}{3}-0,25\right)}{5\left(0,5+\frac{1}{3}-0,25\right)}=-\frac{3}{5}+\frac{3}{5}=0\)
sao bạn tự đăng tự giải thế? hay là bạn giải cho ai à?
Tính rồi so sánh từng cặp kết quả sau:
a) \( - \left( {4 + 7} \right)\) và \( - 4 - 7\)
b) \( - \left( {12 - 25} \right)\) và \(\left( { - 12 + 25} \right)\)
c)\( - \left( { - 8 + 7} \right)\) và \(\left( {8 - 7} \right)\)
d) \( + \left( { - 15 - 4} \right)\) và \(\left( { - 15 - 4} \right)\)
e) \( + \left( {23 - 12} \right)\) và \(\left( {23 - 12} \right)\).
a) \( - \left( {4 + 7} \right) = - 11\)
\(\begin{array}{l}\left( { - 4 - 7} \right) = \left( { - 4} \right) + \left( { - 7} \right)\\ = - \left( {4 + 7} \right) = - 11\\ \Rightarrow \left( { - 4 - 7} \right) = - \left( {4 + 7} \right)\end{array}\)
b)
\(\begin{array}{l} - \left( {12 - 25} \right) = - \left[ {12 + \left( { - 25} \right)} \right]\\ = - \left[ { - \left( {25 - 12} \right)} \right] = - \left( { - 13} \right) = 13\end{array}\)
\(\begin{array}{l}\left( { - 12 + 25} \right) = 25 - 12 = 13\\ \Rightarrow - \left( {12 - 25} \right) = \left( { - 12 + 25} \right)\end{array}\)
c)
\(\begin{array}{l} - \left( { - 8 + 7} \right) = - \left[ { - \left( {8 - 7} \right)} \right] = - \left( { - 1} \right) = 1\\\left( {8 - 7} \right) = 1\\ \Rightarrow - \left( { - 8 + 7} \right) = \left( {8 - 7} \right)\end{array}\)
d)
\(\begin{array}{l} + \left( { - 15 - 4} \right) = + \left[ {\left( { - 15} \right) + \left( { - 4} \right)} \right]\\ = + \left[ { - \left( {15 + 4} \right)} \right] = + \left( { - 19} \right) = - 19\\\left( { - 15 - 4} \right) = \left( { - 15} \right) + \left( { - 4} \right)\\ = - \left( {15 + 4} \right) = - 19\\ \Rightarrow + \left( { - 15 - 4} \right) = \left( { - 15 - 4} \right)\end{array}\)
e)
\(\begin{array}{l} + \left( {23 - 12} \right) = + 11 = 11\\\left( {23 - 12} \right) = 11\\ \Rightarrow + \left( {23 - 12} \right) = \left( {23 - 12} \right)\end{array}\)