{"questions":[{"content":"Вычислите:<br />$3^{n}$, если $n=1;\\space 3;\\space 6$.[[input-1]][[input-10]][[input-18]]","widgets":{"input-1":{"type":"input","unit":"при $\\space n=1$","answer":"3"},"input-10":{"type":"input","unit":"при $\\space n=3$","answer":"27"},"input-18":{"type":"input","unit":"при $\\space n=6$","answer":"729"}}},{"content":"Вычислите:<br />$a^{5}$, если $a=-1;\\space 0.2; \\space 10$.[[input-68]][[input-88]][[input-118]]","widgets":{"input-68":{"type":"input","unit":"при $\\space a=-1$","answer":["-1","минус 1","- 1"]},"input-88":{"type":"input","unit":"при $\\space a=0.2$","answer":["0.00032","0,00032"]},"input-118":{"type":"input","unit":"при $\\space a=10$","answer":"100000"}}},{"content":"Представьте данные числа в виде квадрата некоторого числа:<br />$16; \\space 64;\\space 0.81$.[[input-166]][[input-219]][[input-243]]","widgets":{"input-166":{"type":"input","unit":"$^{2}\\space=16$","answer":["4","-4"]},"input-219":{"type":"input","unit":"$^{2}\\space=64$","answer":["8","-8"]},"input-243":{"type":"input","unit":"$^{2}\\space=0.81$","answer":["0.9","-0,9"]}}},{"content":"Представьте данные числа в виде куба некоторого числа:<br />$-1;\\space 125;\\space-0.216$.[[input-414]][[input-454]][[input-487]]","widgets":{"input-414":{"type":"input","unit":"$^{3}\\space = -1$","answer":"-1"},"input-454":{"type":"input","unit":"$^{3}\\space=125$","answer":"5"},"input-487":{"type":"input","unit":"$^{3}\\space=-0.216$","answer":["-0.6","-0,6"]}}},{"content":"Вычислите: <br />$3\\cdot(-4)^{2}=\\space$[[input-654]]<br />$(-2)^{5}\\cdot 3=\\space$[[input-783]]<br />$8^{1}\\cdot 7^{1}=\\space$[[input-866]]","widgets":{"input-654":{"type":"input","inline":1,"answer":"48"},"input-783":{"type":"input","inline":1,"answer":"-96"},"input-866":{"type":"input","inline":1,"answer":"56"}}},{"content":"Вычислите:<br /> <br />$\\cfrac{0.2^{4}}{40}=\\space$[[input-1074]] $\\space\\space\\space\\cfrac{1.8}{(0.3)^{2}}=\\space$[[input-1377]]$\\space\\space\\space\\cfrac{1}{-0.1^{3}}=\\space$[[input-1729]]","widgets":{"input-1074":{"type":"input","inline":1,"answer":["0.00004","0,00004"]},"input-1377":{"type":"input","inline":1,"answer":"20"},"input-1729":{"type":"input","inline":1,"answer":"-1000"}},"step":1,"hints":["$\\cfrac{0.2^{4}}{40}=\\cfrac{0.0016}{40}=0.00004$","$\\cfrac{1.8}{(0.3)^{2}}=\\cfrac{1.8}{0.09}=20$","$\\cfrac{1}{-0.1^{3}}=\\cfrac{1}{-0.001}=-1000$"]},{"content":"Вычислите:<br /><br />$\\Big(\\cfrac{1}{6}\\Big)^{2}\\cdot 36+(-0.1)^{4}\\cdot5000$[[input-1925]]","widgets":{"input-1925":{"type":"input","answer":["1.5","1,5"]}},"step":1,"hints":["Упрощаем часть выражения:<br />$\\Big(\\cfrac{1}{6}\\Big)^{2}\\cdot 36=\\cfrac{1^{2}}{6^{2}}\\cdot36=\\cfrac{1}{36}\\cdot 36=1$","Упрощаем другую часть выражения:<br />$(-0.1)^{4}\\cdot 5000=0.0001\\cdot 5000=0.5$","Складываем полученные результаты:<br />$1+0.5=1.5$<br />Ответ: $1.5$"]}],"mix":1}
