tính (11.3^7.9^7-9^15):(2.3^14)^2
tính (11.3^7.9^7-9^15):(2.3^14)^2
\(\dfrac{11\cdot3^7\cdot9^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
\(=\dfrac{11\cdot3^7\cdot3^{14}-3^{30}}{2^2\cdot3^{28}}\)
\(=\dfrac{3^{21}\left(11-3^9\right)}{2^2\cdot3^{28}}\)
\(=\dfrac{11-3^9}{2^2\cdot3^7}\)
(4^17 + 4^3) : (4^16 + 4^2 )
\(\dfrac{4^{17}+4^3}{4^{16}+4^2}=\dfrac{4^3\left(4^{14}+1\right)}{4^2\left(4^{14}+1\right)}=\dfrac{4^3}{4^2}=4\)
\(\dfrac{4^{17}+4^3}{4^{16}+4^2}=\dfrac{4^3\left(4^{14}+1\right)}{4^2\left(4^{14}+1\right)}=4\)
B=\(\dfrac{\dfrac{1}{2020}+\dfrac{1}{2021}-\dfrac{1}{2022}}{\dfrac{3}{2020}+\dfrac{3}{2021}-\dfrac{3}{2022}}-1\)
\(B=\dfrac{\dfrac{1}{2020}+\dfrac{1}{2021}-\dfrac{1}{2022}}{\dfrac{3}{2020}+\dfrac{3}{2021}-\dfrac{3}{2022}}-1=\dfrac{\dfrac{1}{2020}+\dfrac{1}{2021}-\dfrac{1}{2022}}{3\left(\dfrac{1}{2020}+\dfrac{1}{2021}-\dfrac{1}{2022}\right)}-1=\dfrac{1}{3}-1=-\dfrac{2}{3}\)
\(B=\dfrac{\dfrac{1}{2021}+\dfrac{1}{2021}-\dfrac{1}{2022}}{\dfrac{3}{2020}+\dfrac{3}{2021}-\dfrac{3}{2022}}-1=\dfrac{\dfrac{1}{2021}+\dfrac{1}{2021}-\dfrac{1}{2022}}{3\left(\dfrac{1}{2020}+\dfrac{1}{2021}-\dfrac{1}{2022}\right)}-1=\dfrac{1}{3}-1=\dfrac{1}{3}-\dfrac{3}{3}=-\dfrac{2}{3}\)
(23.94+93+45):(92.10-92)
các bn giúp mik vs ạ!
cảm ơn các bn rất nh!!!!
\(\left(2^3\cdot9^4+9^3+45\right):\left(9^2\cdot10-9^2\right)\)
\(=\dfrac{9^3\cdot\left(2^3\cdot9+1\right)+45}{9^3}\)
\(=\dfrac{9^3\cdot73+45}{9^3}=\dfrac{5918}{81}\)
(\(\dfrac{a-b}{c-d}\))4=(\(\dfrac{a^4+b^4}{c^4+d^4}\))
(4/7-1/3)^x=8 giúp mik câu này vs
Ta có: \(\left(\dfrac{4}{7}-\dfrac{1}{3}\right)^x=8\)
\(\Leftrightarrow\left(\dfrac{5}{21}\right)^x=8\)
Tìm giá trị nhỏ nhất của các biểu thức sau:
a) A = x\(^2\) + 3
b) B = (2x + 1)\(^2\) - 5
c) C = (2x - 1)\(^{2008}\) + (3y - 2)\(^{2008}\)
a)Ta có: \(x^2\ge0\Rightarrow x^2+3\ge3\)
Dấu "=" xảy ra \(\Leftrightarrow x=0\)
Vậy \(A_{Min}=3 khi x=0\)
b) \(\left(2x+1\right)^2\ge0\Rightarrow\left(2x+1\right)^2-5\ge-5\)
Dấu "=" xảy ra \(\Leftrightarrow x=-\dfrac{1}{2}\)
Vậy \(B_{Min}=-5khix=-\dfrac{1}{2}\)
c) \(\left(2x-1\right)^{2008}\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)
\(\left(3y-2\right)^{2008}\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow y=\dfrac{2}{3}\)
\(\Rightarrow\left(2x-1\right)^{2008}+\left(3y-2\right)^{2008}\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{2}{3}\end{matrix}\right.\)
Vậy \(C_{Min}=0khix=\dfrac{1}{2}vày=\dfrac{2}{3}\)
(-3) mũ n /81=-27
tìm n
Ta có: \(\dfrac{\left(-3\right)^n}{81}=-27\)
\(\Leftrightarrow\left(-3\right)^n=-243\)
hay n=5
so sanh
(-1/16) mu 100 va (-1/2) mu 500
(1/81) mu 12 va (1/27) mu 16
(-2) mu 10 va 1000
2 mu 93 va 5 mu 35
a: \(\left(-\dfrac{1}{16}\right)^{100}=\left(\dfrac{1}{16}\right)^{100}=\left(-\dfrac{1}{2}\right)^{400}\)
\(\left(-\dfrac{1}{2}\right)^{500}=\left(-\dfrac{1}{2}\right)^{500}\)
mà \(400< 500\)
nên \(\left(-\dfrac{1}{16}\right)^{100}< \left(-\dfrac{1}{2}\right)^{500}\)
Giúp mk với!
Viết biểu thức dưới dạng 1 lũy thừa
a)64\(^2\).32\(^4\) b)11\(^{16}\).5\(^{24}\)
a) \(64^2\cdot32^4=2^{16}\cdot2^{20}=2^{36}\)
b) \(11^{16}\cdot5^{24}=\left(11^4\right)^4\cdot\left(5^6\right)^4=\left(11^4\cdot5^6\right)^4\)
a)642.324=(26)2.(25)4=212.220=232
b)1116.524(ko phân tích đc nữa)