Вычислите: а) 2^4; 3^3; 4^4; 5^3; 10^5; 1^7; б) (−5)^2; (−2)^3; (−3)^4; (−10)^7; (−1)^6; (−4)^3; в) (1/2)^4; (−1/3)^3; (1/5)^4; (−3/4)^3; г) (1 2/3)^3; (−1 1/9)^2; (2 1/2)^4; (−3 1/3)^3; д) 0,1^8; (−0,3)^3; 0,2^6; (−0,5)^4; е) 1,5^3; (−2,5)^4; 1,1^2; (−1,2)^3.

Question

Вычислите: а) 2^4; 3^3; 4^4; 5^3; 10^5; 1^7; б) (−5)^2; (−2)^3; (−3)^4; (−10)^7; (−1)^6; (−4)^3; в) (1/2)^4; (−1/3)^3; (1/5)^4; (−3/4)^3; г) (1 2/3)^3; (−1 1/9)^2; (2 1/2)^4; (−3 1/3)^3; д) 0,1^8; (−0,3)^3; 0,2^6; (−0,5)^4; е) 1,5^3; (−2,5)^4; 1,1^2; (−1,2)^3.

Фото задания: Вычислите: а) 2^4; 3^3; 4^4; 5^3; 10^5; 1^7; б) (−5)^2; (−2)^3; (−3)^4; (−10)^7; (−1)^6; (−4)^3; в) (1/2)^4; (−1/3)^3;…

Accepted Answer

Используем определение степени: произведение одинаковых множителей.

а) \(2^4=16\); \(3^3=27\); \(4^4=256\); \(5^3=125\); \(10^5=100000\); \(1^7=1\).
б) \((-5)^2=25\); \((-2)^3=-8\); \((-3)^4=81\); \((-10)^7=-10000000\); \((-1)^6=1\); \((-4)^3=-64\).
в) \(\left(\frac12\right)^4=\frac1{16}\); \(\left(-\frac13\right)^3=-\frac1{27}\); \(\left(\frac15\right)^4=\frac1{625}\); \(\left(-\frac34\right)^3=-\frac{27}{64}\).
г) \(\left(1\frac23\right)^3=\left(\frac53\right)^3=\frac{125}{27}=4\frac{17}{27}\); \(\left(-1\frac19\right)^2=\left(-\frac{10}{9}\right)^2=\frac{100}{81}=1\frac{19}{81}\); \(\left(2\frac12\right)^4=\left(\frac52\right)^4=\frac{625}{16}=39\frac1{16}\); \(\left(-3\frac13\right)^3=\left(-\frac{10}{3}\right)^3=-\frac{1000}{27}=-37\frac1{27}\).
д) \(0{,}1^8=0{,}00000001\); \((-0{,}3)^3=-0{,}027\); \(0{,}2^6=0{,}000064\); \((-0{,}5)^4=0{,}0625\).
е) \(1{,}5^3=3{,}375\); \((-2{,}5)^4=39{,}0625\); \(1{,}1^2=1{,}21\); \((-1{,}2)^3=-1{,}728\).

Ответ: а) 16; 27; 256; 125; 100000; 1. б) 25; −8; 81; −10000000; 1; −64. в) \(\frac1{16}; -\frac1{27}; \frac1{625}; -\frac{27}{64}\). г) \(\frac{125}{27}; \frac{100}{81}; \frac{625}{16}; -\frac{1000}{27}\). д) 0,00000001; −0,027; 0,000064; 0,0625. е) 3,375; 39,0625; 1,21; −1,728.