Viết các biểu thức sau dưới dạng luỹ thừa (an ) với a ∈ Q ; n ∈ Z:
a)\(\frac{1}{81}\)x (\(\frac{1}{3}\))-2 x 9 x 33
b) (25x4) : (23 x \(\frac{1}{16}\))
c) 25 x 32 (\(\frac{3}{2}\))-2
d) (3-2)-2 x 3-5 x 27
e) 99+1; 9999+1; 999...9( m chữ số 9)+1
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\(n=13\Rightarrow n.1=13.1\)
\(\Rightarrow\frac{n}{1}=\frac{13}{1}\)
\(\frac{1}{n}=\frac{1}{13}\)
\(\frac{n}{13}=\frac{1}{1}\)
\(\frac{13}{n}=\frac{1}{1}\)
A=1+2+22+23+...+230A=1+2+22+23+...+230
2A=2+22+23+24+...+2312A=2+22+23+24+...+231
2A−A=231−12A−A=231−1
A=231−1A=231−1
A+1=331
\(2\cdot8^{15}\cdot4\cdot8^{20}=\left(2\cdot4\right)\cdot8^{15+20}=8\cdot8^{35}=8^{36}\)
\(a)12^8\cdot9^{12}\)
\(=\left(2^2\cdot3\right)^8\cdot\left(3^2\right)^{12}\)
\(=\left(2^2\right)^8\cdot3^8\cdot3^{24}\)
\(=2^{16}\cdot3^{32}\)
\(=2^{16}\cdot\left(3^2\right)^{16}\)
\(=2^{16}\cdot9^{16}\)
\(=\left(2\cdot9\right)^{16}\)
\(=18^{16}\)
\(A=9^{25}.27^4.81^3=\left(3^2\right)^{25}.\left(3^3\right)^4.\left(3^4\right)^3=3^{50}.3^{12}.3^{12}=3^{74}\)
k mk nhé
\(2^5.8^4=2^5.\left(2^3\right)^4=2^5.2^{12}=2^{17}\)
\(25^6.125^3=\left(5^2\right)^6.\left(5^3\right)^3=5^{12}.5^9=5^{21}\)
1- 2x2x2x2x2
2-8x8x8x8
3- 25x25x25x25x25x25
4- 125x125x125
a) \(\frac{1}{81}\times\left(\frac{1}{3}\right)^{-2}\times9\times3^3\)
\(=\frac{3^7}{3^4}\)
\(=3^3\)
b) \(\left(2^5\times4\right)\div\left(2^3\times\frac{1}{16}\right)\)
\(=2^7\div\frac{2^3}{2^{\text{4}}}\)
\(=2^7\div\frac{1}{2}\)
=\(2^6\)