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a. \(\left(2^9.16+2^9.34\right):2^{16}\)
\(=2^9\left(17+34\right):2^{16}\)
\(=50:2^7\)
=\(\dfrac{50}{128}=\dfrac{25}{64}=\left(\dfrac{5}{8}\right)^2\)
b. \(\left(3^4.57-9^2.21\right):3^5\)
\(=\left(3^4.3.19-3^4.3.7\right):3^5\)
\(=\left(3^5.19-3^5.7\right):3^5\)
\(=3^5.\left(19-7\right):3^5\)
=12
\(\left[\left(3^4.57\right)-9^2.21\right]:2^5\)
\(=\left(3^4.3.19-3^4.3.7\right):2^5\)
\(=\left[3^5\left(19-7\right)\right]:2^5\)
\(=\left(3^5.12\right):2^5\)
\(=\left(3^5.3.2^2\right):2^5\)
\(=\left(3^6.2^2\right):2^5\)
\(=\frac{3^6.2^2}{2^5}\)
\(=\frac{3^6}{2^3}\)
\(=\frac{729}{8}\)
=(81*57-81*21)/25
=(81*(57-21)/25
=(81*36)/32
=2916/32
=91.215
Trả lời:
a) \(4^{10}.8^{15}=\left(2^2\right)^{10}.\left(2^3\right)^{15}\)
\(=2^{20}.2^{45}\)
\(=2^{65}\)
\(a,4^{10}\cdot8^{15}=\left[2^2\right]^{10}\cdot\left[2\cdot2^2\right]^{15}=2^{20}\cdot2^{15}\cdot2^{30}=2^{20+15+30}=2^{65}\)
\(b,\frac{27^{16}}{3^{10}}=\frac{\left[3^3\right]^{16}}{3^{10}}=\frac{3^{48}}{3^{10}}=3^{48-10}=3^{38}\)
\(c,\frac{\left[2^9\cdot16+2^9\cdot34\right]}{2^{10}}=\frac{\left[2^9\left\{16+34\right\}\right]}{2^{10}}=\frac{2^9\cdot50}{2^{10}}=\frac{1}{2}\cdot50=25\)
\(d,\frac{3^4\cdot57-9^2\cdot21}{3^5}=\frac{3^4\cdot57-\left[3^2\right]^2\cdot21}{3^5}=\frac{3^4\cdot57-3^4\cdot21}{3^5}=\frac{3^4\left[57-21\right]}{3^5}=\frac{1}{3}\cdot36=12\)
(34.57-92.21):35
=(81.57-81.21):243
=[81.(57-21)]:243
=(81.36):243
=2916:243
=12
\(\left(3^4.57-9^2.21\right):3^5\)
\(=\left(81.57-81.21\right):243\)
\(=\left(81\left(57-21\right)\right):243\)
\(=\left(81.36\right):243\)
\(=2916:243\)
\(=12\)
\(A,\frac{4^9.36+64}{16^4.100}=\frac{\left(2^2\right)^9.2^2.3^2+2^6}{\left(2^4\right)^4.2^2.5^2}=\frac{2^{20}.3^2+2^6}{2^{18}.5^2}=\frac{2^6\left(2^{14}.3^2+1\right)}{2^{18}.5^2}=\frac{2^{14}.3^2+1}{2^{12}.5^2}=\frac{147457}{102400}\)
B,
\(\frac{11.3^{22}.3-9^{13}}{\left(2.3^{14}\right)^2}=\frac{11.3^{22}-\left(3^2\right)^{13}}{2^2.3^{28}}=\frac{11.3^{22}-3^{26}}{2^2.3^{28}}=\frac{3^{22}\left(11.1-3^4\right)}{2^2.3^{28}}=\frac{11-81}{2^2.3^6}=-\frac{70}{2916}=-\frac{35}{1456}\)
c,
\(\frac{45^3.20^4.18}{180^5}=\frac{\left(3^2.5\right)^3.\left(5.2^2\right)^4.2.3^2}{\left(2^2.3^2.5\right)^5}=\frac{3^6.5^3.5^4.2^8.2.3^2}{2^{10}.3^{10}.5^5}=\frac{3^8.2^{10}.5^7}{2^{10}.3^{10}.5^5}=\frac{5^2}{3^2}=\frac{25}{9}\)
\(\frac{4^9\cdot36+64}{16^4\cdot100}=\frac{2^6\cdot147457}{2^{16}\cdot100}=\frac{147457}{2^{10}\cdot100}\)
\(\frac{11\cdot3^{22}\cdot3-9^{13}}{2^2\cdot3^{28}}=\frac{3^{23}\left(11-3^3\right)}{2^2\cdot3^{28}}=\frac{-16\cdot3^{23}}{2^2\cdot3^{28}}=\frac{-4}{243}\)
\(\frac{45^3\cdot20^4\cdot18}{180^5}=\frac{3^8\cdot2^9\cdot5^7}{2^{10}\cdot3^{10}\cdot5^5}=\frac{25}{18}\)
\(\left(3^4\cdot57-9^2\cdot21\right):3^5\)
\(=\)\(\left(3^4\cdot57-\left(3^2\right)^2\cdot21\right):3^5\)
\(=\)\(\left(3^4\cdot57-3^4\cdot21\right):3^5\)
\(=\)\(\left(3^4\cdot\left(57-21\right)\right):3^5\)
\(=\)\(\left(81\cdot36\right):243\)
\(=\)\(2916:243\)
\(=\)\(12\)