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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) \(\left(-\frac{1}{3}\right)^5:\left(\frac{1}{6}\right)^5=\left(-2\right)^5=-32\)
\(\dfrac{81}{125}-\dfrac{8}{27}=\dfrac{3^4}{5^3}-\dfrac{2^3}{3^3}\)
a) \(\left(\frac{27}{64}\right)^8:\left(\frac{3}{4}\right)^{22}=\left[\left(\frac{3}{4}\right)^3\right]^8:\left(\frac{3}{4}\right)^{22}=\left(\frac{3}{4}\right)^{24}:\left(\frac{3}{4}\right)^{22}=\left(\frac{3}{4}\right)^2\)
b) \(\left(\frac{2}{3}\right)^2.\left(-\frac{8}{27}\right).\left(-\frac{2}{3}\right)=\left(\frac{2}{3}\right)^2.\left(-\frac{2}{3}\right)^3.\left(-\frac{2}{3}\right)=\left(\frac{2}{3}\right)^2.\left(-\frac{2}{3}\right)^4=\left(\frac{2}{3}\right)^6\)
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!
d)\(-\frac{8}{27}=\frac{\left(-2\right)^3}{3^3}=\left(-\frac{2}{3}\right)^3\)
h)\(-\frac{27}{64}=\frac{\left(-3\right)^3}{4^3}=\left(-\frac{3}{4}\right)^3\)
\(\frac{-8}{27}=\frac{\left(-2\right)^3}{3^3}\)
\(\frac{-27}{64}=\frac{-3^3}{4^3}\)
\(a,=\frac{2}{3}.\frac{2^2}{3^2}.\frac{2^3}{3^3}=\frac{2.2^2.2^3}{3.3^2.3^3}=\frac{2^6}{3^6}\)
\(b,=\frac{3}{4}.\frac{3^2}{4^2}.\frac{3^3}{4^3}=\frac{3.3^2.3^3}{4.4^2.4^3}=\frac{3^6}{4^4}\)
-8/27 = (-2/3)3 nha còn cái kia mình cụng ko bít đâu mình cũng đang hỏi
a) \(2^{27}=\left(2^3\right)^9=8^9\)
\(3^{18}=\left(3^2\right)^9=9^9\)
b) ta có : \(2^{27}=\left(2^3\right)^9=8^9và3^{18}=\left(3^2\right)^9=9^9\)
vì : \(8^9< 9^9\)
nên: \(2^{27}< 3^{18}\)
a) \(2^{27}=\left(2^3\right)^9=8^9;3^{18}=\left(3^2\right)^9=9^9\)
b) Vì 89 < 99 => 227 < 318 nên 318 là số lớn hơn
\(2^6\)\(0,5^2\)\(\left(\frac{1}{2}\right)^4\)\(\left(\frac{1}{2}\right)^8\)\(\left(\frac{11}{12}\right)^2\)