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\(a\)) \(\left(4^2.4^3\right):2^{10}\)
\(=4^5:2^{10}\)
\(=\left(2^2\right)^5:2^{10}\)
\(=2^{10}:2^{10}\)
\(=1\)
\(b\)) \(\left(0,6\right)^5:\left(0,2\right)^6\)
\(=\left(\frac{3}{5}\right)^5:\left(\frac{1}{5}\right)^6\)
\(=\frac{3^5}{5^5}:\frac{1^6}{5^6}\)
\(=\frac{3^5}{5^5}.5^6\)
\(=\frac{3^5.5^6}{5^5}\)
\(=3^5.5\)
\(=243.5\)
\(=1215\)
\(c\)) \(\left(2^7.9^3\right):\left(6^5.8^2\right)\)
\(=\left[2^7.\left(3^2\right)^3\right]:\left[\left(2.3\right)^5.\left(2^4\right)^2\right]\)
\(=\left(2^7.3^6\right):\left[2^5.3^5.2^8\right]\)
\(=\left(2^7.3^6\right).\left(\frac{1}{2^5.3^5.2^8}\right)\)
\(=\frac{2^7.3^6.1}{\left(2^5.2^8\right).3^5}\)
\(=\frac{2^7.3^6}{2^{13}.3^5}\)
\(=\frac{3}{2^6}\)
\(=\frac{3}{64}\)
\(\left|2x-1\right|=\dfrac{3}{2}\\ \Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{3}{2}\\2x-1=-\dfrac{3}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
Thay \(x=\dfrac{5}{4}\) vào D ta có:
\(D=4x+3=4.\dfrac{5}{4}+3=5+3=8\)
Thay \(x=-\dfrac{1}{4}\) vào D ta có:
\(D=4.\dfrac{-1}{4}+3=-1+3=2\)
Để \(D=\dfrac{3}{2}\)
\(\Leftrightarrow4x+3=\dfrac{3}{2}\\ \Leftrightarrow4x=-\dfrac{3}{2}\\ \Leftrightarrow x=-\dfrac{3}{8}\)
A = \(\dfrac{1+5+5^2+5^3+5^4+...+5^{17}}{1+5^2+5^4+...+5^{16}}\)
Đặt tử số là B = 1 + 5 + 52 + 53 + 54 +...+ 517
5B = 5 + 52 + 53 + 54 +...+ 517 + 518
5B - B = 518 - 1
4B = 518 - 1
B = (518 - 1) : 4
Đặt mẫu số là C = 1 + 52 + 54 +...+ 516
52.C = 52 + 54 +...+ 516 + 518
25.C - C = 518 - 1
24C = 518 - 1
C = (518 - 1): 24
A = \(\dfrac{B}{C}\) = \(\dfrac{\dfrac{5^{18}-1}{4}}{\dfrac{5^{18}-1}{24}}\)
A = 6
\(\dfrac{8^2.4^5}{2^{20}}\) = \(\dfrac{\left(2^3\right)^2\left(2^2\right)^5}{2^{20}}\) = \(\dfrac{2^6.2^{10}}{2^{20}}\) = \(\dfrac{2^{16}}{2^{20}}\) = \(\dfrac{1}{2^4}\) = \(\dfrac{1}{16}\)
