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a) \(\frac{16.64.8^2}{4^3.2^5.16}=\frac{16.4^3.\left(2^3\right)^2}{4^3.2^5.16}=\frac{16.4^3.2^6}{4^3.2^5.16}=2\)
\(\frac{64^2.81^3.34}{2^{13}.3^9.17}=\frac{\left(2^6\right)^2.\left(3^4\right)^3.2.17}{2^{13}.3^9.17}=\frac{2^{13}.3^{12}.17}{2^{13}.3^9.17}=3^3=27\)
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a) ( x-140):7=33 -23 -3
(x-140):7 = 27 - 8-3
(x-140):7 = 16
(x-140):7 = 16 .7
x-140 = 112
x-140 = 112+ 140
x = 252

\(3^5\cdot3^2\cdot3=3^{\left(5+2+1\right)}=3^8\)
\(16^4:4^2=\left(4^2\right)^4:4^2=4^8:4^2=4^6\)
\(2^5:16=2^5:2^4=2\)
\(4^2:2^4=\left(2^2\right)^2:2^4=\frac{2^4}{2^4}=1\)
\(3^5.3^2.3=3^7.3=3^8\)
\(16^4:4^2=16^4:16=16^3\)
\(a:a=19:17=\frac{19}{17}\)
\(2^5:16=2^5:2^4=2\)
\(4^4:2^4=\left(2^2\right)^4:2^4=2^6:2^4=2^2=4\)

Giải:
a) \(4.2^5:\left(2^3.\dfrac{1}{16}\right)\)
\(=4.2^5:\dfrac{2^3}{16}\)
\(=2^2.2^5:\dfrac{2^3}{2^4}\)
\(=2^7:\dfrac{1}{2}\)
\(=2^6=64\)
Vậy ...
b) \(\dfrac{8^5.10^4.25^3}{16^4.625^3}\)
\(=\dfrac{2^{15}.2^4.5^4.5^6}{2^8.5^{12}}\)
\(=\dfrac{2^{19}.5^{10}}{2^8.5^{12}}\)
\(=\dfrac{2^{11}}{5^2}\)
Vậy ...
c) \(C=2^{200}-2^{199}+2^{198}-2^{197}+...+2^2-2\)
\(\Leftrightarrow C=\left(2^{200}-2^{199}\right)+\left(2^{198}-2^{197}\right)+...+\left(2^2-2\right)\)
\(\Leftrightarrow C=2^{199}\left(2-1\right)+2^{197}\left(2-1\right)+...+2\left(2-1\right)\)
\(\Leftrightarrow C=2^{199}+2^{197}+...+2\)
\(\Leftrightarrow4C=2^{201}+2^{199}+...+2^3\)
\(\Leftrightarrow3C=4C-C=2^{201}-2\)
\(\Leftrightarrow C=\dfrac{2^{201}-2}{3}\)
Vậy ...
16.64.82:(43.25.16)
=24.26.26:(26.25.24)
=24.26.26:215
=216:215
=2