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МатематикаРешебник по алгебре 7 класс Мерзляк ФГОС Задание 236
Задание 236
\[\boxed{\text{236\ (236).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \left( 6^{4} \right)^{4}\ :\left( 6^{5} \right)^{3} = 6^{16}\ :6^{15} =\]
\[= 6^{1} = 6\]
\[2)\ 8^{3}\ :4^{4} = \left( 2^{3} \right)^{3}\ :\left( 2^{2} \right)^{4} =\]
\[= 2^{9}\ :2^{8} = 2^{1} = 2\]
\[3)\ \frac{7^{14} \cdot \left( 7^{2} \right)^{3}}{\left( 7^{3} \right)^{6} \cdot 7^{2}} = \frac{7^{14} \cdot 7^{6}}{7^{18} \cdot 7^{2}} = \frac{7^{20}}{7^{20}} =\]
\[= 1\]
\[4)\ \frac{25^{3} \cdot 125^{2}}{5^{10}} = \frac{\left( 5^{2} \right)^{3} \cdot \left( 5^{3} \right)^{2}}{5^{10}} =\]
\[= \frac{5^{6} \cdot 5^{6}}{5^{10}} = \frac{5^{12}}{5^{10}} = 5^{2} = 25\]
\[5)\ \frac{3^{8} \cdot 7^{8}}{21^{7}} = \frac{(3 \cdot 7)^{8}}{21^{7}} = \frac{21^{8}}{21^{7}} =\]
\[= 21\]
\[6)\ \frac{5^{9} \cdot 4^{6}}{20^{6}} = \frac{5^{3} \cdot 5^{6} \cdot 4^{6}}{20^{6}} =\]
\[= \frac{5^{3} \cdot 20^{6}}{20^{6}} = 5^{3} = 125\]
\[\boxed{\text{236.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
| \[a\] | \[- 6\] | \[6\] | \[- 0,4\] | \[0,4\] | \[3\] | \[0,03\] | \[\frac{1}{2}\] | \[- 1\] | \[0\] |
|---|---|---|---|---|---|---|---|---|---|
| \[10a^{2}\] | \[360\] | \[360\] | \[1,6\] | \[1,6\] | \[90\] | \[0,009\] | \[2,5\] | \[10\] | \[0\] |
| \[(10a)^{2}\] | \[3600\] | \[3600\] | \[16\] | \[16\] | \[900\] | \[0,09\] | \[25\] | \[100\] | \[0\ \ \] |
Решение.
\[(10 \cdot 6)^{2} = 60^{2} = 3600.\]
\[10 \cdot 6^{2} = 10 \cdot 36 = 360\text{.\ }\]
\[\left( 10 \cdot ( - 6) \right)^{2} = ( - 60)^{2} = 3600.\]
\[10 \cdot ( - 6)^{2} = 10 \cdot 36 = 360.\ \]
\[\left( 10 \cdot ( - 0,4) \right)^{2} = ( - 4)^{2} = 16.\]
\[10 \cdot ( - 0,4)^{2} = 10 \cdot 0,16 = 1,6.\ \]
\[\left( 10 \cdot (0,4) \right)^{2} = (4)^{2} = 16.\]
\[10 \cdot (0,4)^{2} = 10 \cdot 0,16 = 1,6.\ \]
\[(10 \cdot 3)^{2} = (30)^{2} = 900.\]
\[10 \cdot 3^{2} = 10 \cdot 9 = 90.\ \]
\[\left( 10 \cdot (0,03) \right)^{2} = (0,3)^{2} = 0,09.\]
\[10 \cdot (0,03)^{2} = 10 \cdot 0,0009 =\]
\[= 0,009.\ \]
\[\left( 10 \cdot \left( \frac{1}{2} \right) \right)^{2} = (5)^{2} = 25.\]
\[10 \cdot \left( \frac{1}{2} \right)^{2} = 10 \cdot \frac{1}{4} = \frac{10}{4} = 2,5.\ \]
\[\left( 10 \cdot ( - 1) \right)^{2} = ( - 10)^{2} = 100.\]
\[10 \cdot ( - 1)^{2} = 10 \cdot 1 = 10.\ \]
\[(10 \cdot 0)^{2} = (0)^{2} = 0.\]
\[10 \cdot 0^{2} = 0.\ \]
