№ 9.15 Алгебра = № 19.15 Математика
Знайдіть значення виразу:
1. $ \ -64\cdot4^{-4};$
2. $\ 36\cdot\left(-27\right)^{-1};$
3. $-7\cdot{0{,}1}^{-2}+5^0.$
4. $\ -3\frac{1}{6}\cdot\left(-\frac{1}{6}\right)^{-1};$
5. $\ 5^{-2}-{10}^{-1};$
6. $\ {3{,}2}^{-1}+\left(1\frac{1}{3}\right)^{-2};$
7. $\left(\frac{1}{5}\right)^{-3}\cdot{20}^{-2};$
8. $\left(\frac{3}{8}\right)^{-2}\cdot\left(\frac{2}{3}\right)^{-4}$
9. $\ {1{,}5}^{-2}-{1{,}2}^{-3}.$
Розв'язок:
1. $-64\cdot4^{-4}=-\frac{64}{4^4}=-\frac{4^3}{4^4}=$
$= -\frac{1}{4};$
2. $36\cdot\left(-27\right)^{-1}=36\cdot\left(-\frac{1}{27}\right)=$
$= -\frac{36}{27}=-\frac{4}{3}=-1\frac{1}{3};$
3. $-7\cdot{0{,}1}^{-2}+5^0=-7\cdot\left(\frac{1}{10}\right)^{-2}+1=$
$= -7\cdot100+1=-700+1=-699;$
4. $-3\frac{1}{6}\cdot\left(-\frac{1}{6}\right)^{-1}=$
$= -\frac{19}{6}\cdot\left(-6\right)=19;$
5. $5^{-2}-{10}^{-1}=\frac{1}{5^2}-\frac{1}{10}=$
$= \frac{1}{25}-\frac{1}{10}=\frac{2-5}{50}=-\frac{3}{50};$
6. ${3{,}2}^{-1}+\left(1\frac{1}{3}\right)^{-2}=$
$= \left(3\frac{1}{5}\right)^{-1}+\left(\frac{4}{3}\right)^{-2}=$
$= \left(\frac{16}{5}\right)^{-1}+\left(\frac{3}{4}\right)^2=$
$= \frac{5}{16}+\left(\frac{3}{4}\right)^2=\frac{5}{16}+\frac{9}{16}=$
$= \frac{14}{16}=\frac{7}{8};$
7. $\left(\frac{1}{5}\right)^{-3}\cdot{20}^{-2}=5^3\cdot\frac{1}{{20}^2}=$
$= \frac{5^3}{\left(4\cdot5\right)^2}=\frac{5^3}{4^2\cdot5^2}=\frac{5}{4^2}=\frac{5}{16};$
8. $\left(\frac{3}{8}\right)^{-2}\cdot\left(\frac{2}{3}\right)^{-4}=\left(\frac{8}{3}\right)^2\cdot\left(\frac{3}{2}\right)^4=$
$=\frac{64}{9}\cdot\frac{81}{16}=\frac{4}{1}\cdot\frac{9}{1}=36;$
9. ${1{,}5}^{-2}-{1{,}2}^{-3}=$
$= \left(1\frac{1}{2}\right)^{-2}-\left(1\frac{1}{5}\right)^{-3}=$
$= \left(\frac{3}{2}\right)^{-2}-\left(\frac{6}{5}\right)^{-3}=$
$= \left(\frac{2}{3}\right)^2-\left(\frac{5}{6}\right)^3=$
$=\frac{4}{9}-\frac{125}{216}=\frac{96-125}{216}=-\frac{29}{216}.$