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Ta có :
\(0,0\left(8\right)=\frac{4}{45}\)
\(0,1\left(2\right)=\frac{11}{90}\)
\(0,1\left(23\right)=\frac{61}{495}\)
Ta có:
\(0,0\left(8\right)=0,0\left(1\right).8=\frac{0,\left(1\right)}{10}.8=\frac{1}{90}.8=\frac{8}{90}\)
Tương tự hết!
0,0(8) = \(\frac{1}{10}\).0,(8) = \(\frac{1}{10}.\frac{8}{9}=\frac{4}{45}\)
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)
\(\frac{32\cdot2^4}{2^2\cdot\frac{1}{16}}\)
\(=\frac{2^5\cdot2^4}{\frac{4}{16}}\)
\(=\frac{2^9}{\frac{1}{4}}\)
\(=2^9\cdot4\)
\(=2^9\cdot2^2\)
\(=2^{11}\)
=(3^2)^3.(2^3)^7/(2.3)^9.(2^4)^2
=3^6.2^21/2^9.3^9.2^8
=1.2^4/1.3^3.1
=16/27
a: \(1=4^0\)
\(4=4^1\)
\(16=4^2\)
\(256=4^4\)
b: \(\dfrac{1}{4}=4^{-1}\)
\(\dfrac{1}{64}=4^{-3}\)
\(\dfrac{1}{256}=4^{-4}\)
\(\dfrac{1}{16}=4^{-2}\)
\(\dfrac{1}{1024}=4^{-5}\)
\(\frac{8^3\cdot32^5}{64^7}=\frac{\left(2^3\right)^3\cdot\left(2^5\right)^5}{\left(2^6\right)^7}=\frac{2^9\cdot2^{25}}{2^{42}}\)\(=\frac{2^{34}}{2^{42}}=\frac{1}{2^8}=\frac{1}{256}\)