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Ta có :
(0,36)8=(0,6.0,6)8=(0,62)8=0,62.8=0,616
(0,216)4=(0,6.0,6.0,6)4=(0,63)4=0,63.4=0,612
Ta có:
\(\left(0,36\right)^8=\left(0,6.0,6\right)^8=\left(0,6^2\right)^8=0,6^{16}\)
\(\left(0,216\right)^4=\left(0,6.0,6.0,6\right)^4=\left(0,6^3\right)^4=0,6^{12}\)
a) \(x:\left(\frac{3}{4}\right)^3=\left(\frac{3}{4}\right)^2\)
\(x=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3\)
\(x=\left(\frac{3}{4}\right)^5\)
\(x=\frac{243}{1024}\)
vay \(x=\frac{243}{1024}\)
b) \(\left(\frac{2}{5}\right)^5.x=\left(\frac{2}{5}\right)^8\)
\(x=\left(\frac{2}{5}\right)^8:\left(\frac{2}{5}\right)^5\)
\(x=\left(\frac{2}{5}\right)^3\)
\(x=\frac{8}{125}\)
vay \(x=\frac{8}{125}\)
4) \(\left(0,36\right)^8=\left(0,6^2\right)^8=\left(0,6\right)^{16}\)
\(\left(0,216\right)^4=\left(0,6^3\right)^4=\left(0,6\right)^{12}\)
5) a) \(\left(3,5\right)^3=42,875\)
b) \(\left(-\frac{4}{11}\right)^2=\frac{16}{121}\)
c) \(\left(0,5\right)^4.6^4=3^4=81\)
d) \(\left(-\frac{1}{3}\right)^5:\left(\frac{1}{6}\right)^5=\left(-2\right)^5=-32\)
\(2^6\)\(0,5^2\)\(\left(\frac{1}{2}\right)^4\)\(\left(\frac{1}{2}\right)^8\)\(\left(\frac{11}{12}\right)^2\)
1.
a) x : \(\left(\dfrac{3}{4}\right)^3\) =\(\left(\dfrac{3}{4}\right)^3\)
x = \(\left(\dfrac{3}{4}\right)^3.\left(\dfrac{3}{4}\right)^3\)
x = \(\dfrac{3}{4}^{3+3}\)
x = \(\dfrac{3}{4}^6\)
x = \(\dfrac{729}{4096}\)
b) \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
x = \(\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\)
x = \(\dfrac{2}{5}^{8-5}\)
x = \(\dfrac{2}{5}^3\)
x = \(\dfrac{8}{5}\)
2.
(0,36)\(^8\) \([\left(0,6\right)^3]^8\) = (0,6)\(^{3.8}\) = ( 0,6)\(^{24}\)
( 0,216)\(^4\) = \([\left(0,6\right)^3]^4\) = (0.6)\(^{3.4}\) = ( 0,6)\(^{12}\)
\(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)
\(x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\) <=> \(x=\left(\dfrac{3}{4}\right)^{2+3}\)
=> \(x=\left(\dfrac{3}{4}\right)^5\)
b, \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
\(x=\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\Leftrightarrow x=\left(\dfrac{2}{5}\right)^{8-5}\)
=>\(x=\left(\dfrac{2}{5}\right)^3\)
bài 2 : Với bài này ta cần áp dụng quy tắc: \(\left(x^m\right)^n=x^{m.n}\)
\(0,36^8=\left[\left(0,6\right)^2\right]^8=\left(0,6\right)^{16}\)
\(0,216^4=\left[\left(0,6\right)^3\right]^4=\left(0,6\right)^{12}\)
Bài 31 Viết các số và
dưới dạng các lũy thừa của cơ số 0,5
Lời giải:
Ta có:
Giải : Ta có:
(0,25)8 =[(0,5)2]8=(0,5)16
(0,125)4=[(0,5)3]4=(0,5)12
a)Ta có:128=(122)4=1444
812=(83)4=5124
Vì 1444<5124
Suy ra:128<812
b)Ta có:(-5)39=[(-5)3]13=(-125)13
(-2)91=[(-2)7]13=(-128)13
Vì (-128)13<(-125)13
Suy ra:(-2)91<(-5)39
\(a.\) \(12^8\) và \(8^{12}\)
Ta có :
\(12^8=\left(12^2\right)^4=114^4\)
\(8^{12}=\left(8^3\right)^4=512^4\)
Vì \(114^4< 512^4\) nên \(12^8< 8^{12}\)
Vậy : \(12^8< 8^{12}\)
\(b.\) \(\left(-5\right)^{39}\) và \(\left(-2\right)^{91}\)
Ta có :
\(\left(-5\right)^{39}=\left(-5^3\right)^{13}=\left(-125\right)^{13}\)
\(\left(-2\right)^{91}=\left(-2^7\right)^{13}=\left(-128\right)^{13}\)
Vì \(\left(-125\right)^{13}>\left(-128\right)^{13}\) nên \(\left(-5\right)^{39}>\left(-2\right)^{91}\)
7)
\(\left(0,36\right)^8=\left(0,6^2\right)^8=0,6^{16}.\)
8)
a) \(\left(\frac{3}{5}\right)^n=\left(\frac{9}{25}\right)^5\)
\(\Rightarrow\left(\frac{3}{5}\right)^n=\left[\left(\frac{3}{5}\right)^2\right]^5\)
\(\Rightarrow\left(\frac{3}{5}\right)^n=\left(\frac{3}{5}\right)^{10}\)
\(\Rightarrow n=10\)
Vậy \(n=10.\)
b) \(\left(-0,25\right)^p=\frac{1}{256}\)
\(\Rightarrow\left(-0,25\right)^p=\left(\frac{1}{4}\right)^4\)
\(\Rightarrow\left(-0,25\right)^p=\left(0,25\right)^4\)
\(\Rightarrow p=4\)
Vậy \(p=4.\)
Chúc bạn học tốt!
chúc b hok tốt
0,368=(0,62)8=0,616
0,2164=(
hết rùi hả bn