Bài 5: Lũy thừa của một số hữu tỉ
Các câu hỏi tương tự
Viết các biểu thức sau dưới dạng lũy thừa
a) \(2^2.9.\dfrac{1}{54}.\left(\dfrac{4}{9}\right)^2\)
b) \(2^3.2^5.\left(\dfrac{3}{2}\right)^4\)
c) \(\dfrac{\left(\dfrac{1}{2}\right)^3.\dfrac{1}{2^2}.8}{\left(-2^3\right)^2.16}.\left(2^2\right)^3\)
Viết các biểu thức sau dưới dạng lũy thừa
a) \(2^2.9.\dfrac{1}{54}.\left(\dfrac{4}{9}\right)^2\)
b) \(2^3.2^5.\left(\dfrac{3}{2}\right)^4\)
c) \(\dfrac{\left(\dfrac{1}{2}\right)^3.\dfrac{1}{2^2}.8}{\left(-2^3\right)^2.16}.\left(2^2\right)^3\)
Viết các biểu thức số sau dưới dạng \(a^n,\left(a\in\mathbb{Q},n\in\mathbb{N}\right)\) :
a) \(9.3^3.\dfrac{1}{81}.3^2\)
b) \(4.2^5:\left(2^3.\dfrac{1}{16}\right)\)
c) \(3^2.2^5.\left(\dfrac{2}{3}\right)^2\)
d) \(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2\)
Chứng tỏ:
\(\dfrac{1}{3} + \dfrac{1}{3^2} +...+ \dfrac{1}{3^{99}} < \dfrac{1}{2}\)
\(\dfrac{3}{1^2.2^2} + \dfrac{5}{2^2.3^2} + ...+ \dfrac{19}{9^2.10^2}<1 \)
So sánh:
a, \(\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}\) và \(\dfrac{1}{2}\)
b, \(\dfrac{1}{4}-\dfrac{1}{4^2}+\dfrac{1}{4^3}-...+\dfrac{1}{4^{99}}\) và \(\dfrac{1}{12}\)
c, \(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{50}{3^{50}}\) và \(\dfrac{3}{4}\)
Rút gọn biểu thức sau:
B=\(\dfrac{\left(\dfrac{2}{3}\right)^3\times\left(-\dfrac{3}{4}\right)^2\times\left(-1\right)^5}{\left(\dfrac{2}{5}\right)^2\times\left(-\dfrac{5}{12}\right)^3}\)
Tính:
a) S1.2+2.3+3.4+...+99.100
b) Bdfrac{49^{24}.125^{17}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}
c) Cleft(dfrac{1}{3}+dfrac{1}{3^2}+dfrac{1}{3^3}+dfrac{1}{3^4}right).3^5+left(dfrac{1}{3^5}+dfrac{1}{3^6}+dfrac{1}{3^7}+dfrac{1}{3^8}right).3^9+...+left(dfrac{1}{3^{97}}+dfrac{1}{3^{98}}+dfrac{1}{3^{99}}+dfrac{1}{3^{100}}right).3^{101}
d) D 3-3^2+3^3-3^4+...+3^{2017}-3^{2018}
Đọc tiếp
Tính:
a) S=1.2+2.3+3.4+...+99.100
b) B=\(\dfrac{49^{24}.125^{17}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}\)
c) C=\(\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\right).3^5+\left(\dfrac{1}{3^5}+\dfrac{1}{3^6}+\dfrac{1}{3^7}+\dfrac{1}{3^8}\right).3^9+...+\left(\dfrac{1}{3^{97}}+\dfrac{1}{3^{98}}+\dfrac{1}{3^{99}}+\dfrac{1}{3^{100}}\right).3^{101}\)
d) D= \(3-3^2+3^3-3^4+...+3^{2017}-3^{2018}\)
Bài 1:Tính giá trị biểu thức
_{1,}3^2.dfrac{1}{243}.81^2.dfrac{1}{3^3}
_{2,}(4.2^5):left(2^3.dfrac{1}{16}right)
_{3,}left(2^{-1}+3^{-1}right)+left(2^{-1}.2^0right):2^3
_{4,}left(-dfrac{1}{3}right)^{-1}-left(-dfrac{6}{7}right)^0+left(dfrac{1}{2}right)^2:2
_{5,}[(0,1)^2]^0+[(dfrac{1}{7})^{-1}]^2.dfrac{1}{49}.left[left(2^2right)^3:2^5right]
Bài 2:Rút gọn biểu thức
a,dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}
b,dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}
c,left(dfrac{2}{5}right)^7.5^7+left(...
Đọc tiếp
Bài 1:Tính giá trị biểu thức
\(_{1,}\)\(3^2.\dfrac{1}{243}.81^2.\dfrac{1}{3^3}\)
\(_{2,}\)(\(4.2^5\)):\(\left(2^3.\dfrac{1}{16}\right)\)
\(_{3,}\)\(\left(2^{-1}+3^{-1}\right)+\left(2^{-1}.2^0\right):2^3\)
\(_{4,}\)\(\left(-\dfrac{1}{3}\right)^{-1}-\left(-\dfrac{6}{7}\right)^0+\left(\dfrac{1}{2}\right)^2:2\)
\(_{5,}\)[(0,1)\(^2\)]\(^0\)+[(\(\dfrac{1}{7}\))\(^{-1}\)]\(^2\).\(\dfrac{1}{49}.\left[\left(2^2\right)^3:2^5\right]\)
Bài 2:Rút gọn biểu thức
a,\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
b,\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
c,\(\left(\dfrac{2}{5}\right)^7.5^7+\left(\dfrac{9}{4}\right)^3:\left(\dfrac{3}{16}\right)^3\)
\(\overline{2^7.5^2+512}\)
d,\(\left(\dfrac{2}{3}\right)^3.\left(-\dfrac{3}{4}\right)^2.\left(-1\right)^5\)
\(\overline{\left(\dfrac{2}{5}\right)^2}.\left(-\dfrac{5}{12}\right)^3\)
Chứng minh rằng :
\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
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