Dạng 1. Thực hiện phép tính

$a){5.2}^2-18:3$$=5.4-18:3$

$=20-6$$=14$

$b)17.85+15.17-120$$=17.\left(85+15\right)-120$

$=17.100-120$$=1700-120$

$=1580$

$c)2^3.17-2^3.14$ $=2^3\left(17-14\right)$

$=2^3.3$$=8.3$$=24$

$d)20-\left[30-{\left(5-1\right)}^2\right]$

$=20-\left[30-4^2\right]$

$=20-\left(30-16\right)$$=20-14$$=6$

$e)75-\left({3.5}^2-{4.2}^3\right)$

$=75-\left(3.25-4.8\right)$$=75-\left(75-32\right)$

$=75-75+32$$=32$

$f){2.5}^2+3:{71}^0-54:3^3$

$=2.25+3:1-54:27$$=50+3-2$

$=51$

$g)150+50:5-{2.3}^2$

$=150+10-2.9$$=150+10-18$$=142$

$h){5.3}^2-32:4^2$$=5.9-32:16$

$=45-2$$=43$

$a)27.75+25.27-150$

$=27.\left(75+25\right)-150$

$=27.100-150$$=2700-150$

$=2550$

$b)12:\left\{400:\left[500-\left(125+25.7\right)\right]\right\}$

$=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}$

$=12:\left\{400:\left[500-300\right]\right\}$

$=12:\left\{400:200\right\}$$=12:2$$=6$

$c)13.17-256:16+14:7-1$

$=221-16+2-1=221-16+2-1$$=206$

$d)18:3+182+3.\left(51:17\right)$

$=6+182+3.3$$=6+182+9$

$=197$

$e)15-25.8:\left(100.2\right)$

$=15-25.8:200$

$=15-200:200$

$=15-1$=14

$f)25.8-12.5+170:17-8$

$=1000-60+10-8$$=942$

$a)2^3-5^3:5^2+{12.2}^2$

$=8-5+12.4$$=8-5+48$$=51$

$b)5\left[\left(85-35:7\right):8+90\right]-50$

$=5\left[\left(85-5\right):8+90\right]-50$

$=5\left[80:8+90\right]-50$

$=5\left[10+90\right]-50$

$=5.100-50$=450

$c)2.\left[\left(7-3^3:3^2\right):2^2+99\right]-100$

$=2.\left[\left(7-3\right):4+99\right]-100$

$=2.\left(4:4+99\right)-100$

$=2.100-100$=100

$d)2^7:2^2+5^4:5^3{.2}^4-{3.2}^5$

$=2^5+{5.2}^4-{3.2}^5$

$=2^4.\left(2+5-6\right)$$=2^4$

$e)\left(3^5.3^7\right):3^{10}+{5.2}^4–7^3:7$

$=3^{12}:3^{10}+{5.2}^4-7^2$

$=3^2+{5.2}^4-7^2$$=9+5.16-49$

$=9+80-49$=40

$f)3^2.\left[\left(5^2–3\right):11\right]–2^4+{2.10}^3$

$=9.\left[\left(25-3\right):11\right]-16+2.1000$

$=9.\left(22:11\right)-16+2000$

$=9.2-16+2000$$=2+2000=2002$

$g)\left(6^{2007}–6^{2006}\right):6^{2006}$

$=6^{2006}\left(6-1\right):6^{2006}$$=6^{2006}.5:6^{2006}$

=5

$h)\left(5^{2001}-5^{2000}\right):5^{2000}$

$=5^{2000}\left(5-1\right):5^{2000}$

$=5^{2000}.4:5^{2000}$=4

$i)\left(7^{2005}+7^{2004}\right):7^{2004}$

$=7^{2004}(7+1):7^{2004}$

$=7^{2004}.8:7^{2004}$=8

$j)\left(5^7+7^5\right).\left(6^8+8^6\right).\left(2^4–4^2\right)$

$=\left(5^7+7^5\right).\left(6^8+8^6\right).\left(16-16\right)$

$=\left(5^7+7^5\right).\left(6^8+8^6\right).0$=0

$k)\left(7^5+7^9\right).\left(5^4+5^6\right).\left(3^3.3–9^2\right)$

$=\left(7^5+7^9\right).\left(5^4+5^6\right).\left(27-27\right)$

$=\left(7^5+7^9\right).\left(5^4+5^6\right).0$=0

$l)\left[\left(5^2{.2}^3\right)–7^2.2\right):2].6–{7.2}^5$

$=\left[\left(25.8-49.2\right):2\right].6-{7.2}^5$

$=\left(200-98\right):2.6-7.32$$=102:2.6-224$

$=306-224=82$

$a)27.75+25.27-150$

$=27.\left(75+25\right)-150$

$=27.100-150$$=2550$

$b)142-\left[50-\left(2^3.10-2^3.5\right)\right]$

$=142-\left[50-2^3.5\right]$

$=142-5.(10-8)$$=142-10$$=132$

$c)375:\left\{32–\left[4+\left({5.3}^2–42\right)\right]\right\}–14$

$\begin{array}{l}=375:\left\{32-\left[4+\left(45-42\right)\right]\right\}-14\\ =375:\left\{32-\left(4+3\right)\right\}-14\end{array}$

$=375:\left\{32-7\right\}-14$

$=375:25-14$$=15-14$=1

$d)\left\{210:\left[16+3.\left(6+{3.2}^2\right)\right]\right\}–3$

$=\left\{210:\left[16+3.\left(6+12\right)\right]\right\}-3$

$=\left\{210:\left[16+3.18\right]\right\}-3$$=\left\{210:70\right\}-3$

$=3-3=0$

$=500-\left\{5\left[409-{\left(8.3-21\right)}^2\right]-1724\right\}$

$=500-\left\{5.\left[409-{\left(24-21\right)}^2\right]-1724\right\}$

$=500-\left\{5.\left[409-9\right]-1724\right\}$

$=500-\left\{5.400-1724\right\}$

$=500-276$=224

$a)80-\left({4.5}^2-{3.2}^3\right)$

$=80-\left(4.25-3.8\right)$

$=80-\left(100-24\right)$

$=80-76$=4

$b)5^6:5^4+2^3{.2}^2-1^{2017}$

$=5^2+2^5-1$$=25+32-1$

$=56$

$c)125-2.\left[56-48:\left(15-7\right)\right]$

$=125-2.\left[56-48:8\right]$

$=125-2.\left(56-6\right)$

$=125-2.50$=25

$d)23.75+25.10+25.13+180$

$=23.75+25.(10+13)+180$

$=23.75+25.23+180$

$=23.100+180$

$=2300+180$$=2480$

$e)2448:\left[119-\left(23-6\right)\right]$

$=2448:\left[119-17\right]$

$=2448-112$

$=2336$

$f)36.4-4.{\left(82-7.11\right)}^2:4-{2016}^0$

$=36.4-4.{\left(82-77\right)}^2:4-1$$=4\left(36-25\right):4-1$

$=11-1=10$

$g)303-3.\left\{\left[655-\left(18:2+1\right){.4}^3+5\right]\right\}:{10}^0$

$=303-3.\left\{\left[655-\left(9+1\right){.4}^3+5\right]\right\}:1$

$=303-3.\left\{\left[655-640+5\right]\right\}$

$=303-3.10$=263

$A=27.36+73.99+27.14-49.73$

$A=27.36+27.14+73.99-49.73$

$A=27.\left(36+14\right)+73.\left(99-49\right)$

$A=27.50+73.50$

$A=50.\left(27+73\right)$

$A=50.100$=5000

$21.\left(271+29\right)+79.(271+29);$

=$21.300+79.300$

=$300.(21+79)$

=$300.100$=30000

$C=\left(4^5{\mathrm{.10.5}}^6+{25}^5{.2}^8\right):\left(2^8{.5}^4+5^7{.2}^5\right)$

$C=\left(2^{11}{.5}^7+5^{10}{.2}^8\right):\left(2^8{.5}^4+5^7{.2}^5\right)$

$C=\left[2^8{.5}^7.\left(2^3+5^3\right)\right]:\left[2^5{.5}^4.\left(2^3+5^3\right)\right]$

$C=\left(2^8{.5}^7\right):\left(2^5{.5}^4\right)$$=\left(2^8:2^5\right).\left(5^7:5^4\right)$

$C=2^3{.5}^3$$={10}^3$

$D=\left({10}^2+{11}^2+{12}^2\right):\left({13}^2+{14}^2\right)$

$D=\left(100+121+144\right):\left(169+196\right)$

$D=365:365$=1

$\frac{{\left({\mathrm{3.4.2}}^{16}\right)}^2}{{11.2}^{13}{.4}^{11}-{16}^9}$=$\frac{3^2{.2}^4{.2}^{32}}{{11.2}^{13}{.2}^{22}-2^{36}}$

=$\frac{3^2{.2}^{36}}{{11.2}^{35}-2^{36}}$=$\frac{3^2{.2}^{36}}{2^{35}.\left(11-2\right)}$

=$\frac{3^2{.2}^{36}}{2^{35}{.3}^2}=2$