№ 9.6 Алгебра = № 19.6 Математика
Обчисліть:
1. $\ 7^{-2};$
2. $\left(-2\right)^{-2};$
3. $\left(-1\right)^{-5};$
4. $\ {12}^{-1};$
5. $\left(-7\right)^{-1};$
6. $\ {10}^{-3};$
7. $\left(\frac{1}{3}\right)^{-2};$
8. $\left(-\frac{2}{3}\right)^{-1};$
9. $\left(-\frac{3}{4}\right)^{-3};$
10. $\left(1\frac{1}{2}\right)^{-5};$
11. $\left(-1\frac{1}{3}\right)^{-2};$
12. $\left(-2\frac{1}{5}\right)^{-1};$
13. $\ {0,1}^{-1};$
14. $\left(-0,2\right)^{-2};$
15. $\left(1,2\right)^{-2};$
16. $\left(-0,25\right)^{-3}.$
Розв'язок:
1. $\ 7^{-2}=\frac{1}{7^2}=\frac{1}{49};$
2. $\left(-2\right)^{-2}=\frac{1}{\left(-2\right)^2}=\frac{1}{4};$
3. $\left(-1\right)^{-5}=\frac{1}{\left(-1\right)^5}=-1;$
4. $\ {12}^{-1}=\frac{1}{{12}^1}=\frac{1}{12};$
5. $\left(-7\right)^{-1}=\frac{1}{\left(-7\right)^1}=-\frac{1}{7};$
6. $\ {10}^{-3}=\frac{1}{{10}^3}=\frac{1}{1000}=0{,}001;$
7. $\left(\frac{1}{3}\right)^{-2}=3^2=9;$
8. $\left(-\frac{2}{3}\right)^{-1}=-\frac{3}{2}=-1{,}5;$
9. $\left(-\frac{3}{4}\right)^{-3}=\left(-\frac{4}{3}\right)^3=$
$= -\frac{4^3}{3^3}=-\frac{64}{27}=-2\frac{10}{27};$
10. $\left(1\frac{1}{2}\right)^{-5}=\left(\frac{3}{2}\right)^{-5}=$
$= \left(\frac{2}{3}\right)^5=\frac{2^5}{3^5}=\frac{32}{243};$
11. $\left(-1\frac{1}{3}\right)^{-2}=\left(-\frac{4}{3}\right)^{-2}=$
$= \left(-\frac{3}{4}\right)^2=\frac{9}{16};$
12. $\left(-2\frac{1}{5}\right)^{-1}=\left(-\frac{11}{5}\right)^{-1}=$
$= \left(-\frac{5}{11}\right)^1=-\frac{5}{11};$
13. $\ {0,1}^{-1}=\left(\frac{1}{10}\right)^{-1}={10}^1=10;$
14. $\left(-0,2\right)^{-2}=\left(-\frac{2}{10}\right)^{-2}=$
$= \left(-\frac{1}{5}\right)^{-2}=\left(-5\right)^2=25;$
15. $\left(1,2\right)^{-2}=\left(1\frac{2}{10}\right)^{-2}=$
$= \left(1\frac{1}{5}\right)^{-2}=\left(\frac{6}{5}\right)^{-2}=$
$= \left(\frac{5}{6}\right)^2=\frac{25}{36};$
16. $\left(-0,25\right)^{-3}=\left(-\frac{25}{100}\right)^{-3}=$
$= \left(-\frac{1}{4}\right)^{-3}=\left(-4\right)^3=-64.$