Odpowiedź:
[tex]a)~~~~(-6)^{3}\cdot \left(\dfrac{1}{3} \right)^{-2}=-1~944\\\\b)~~~~\left(3\dfrac{1}{4} \right)^{-2}=\dfrac{16}{169}\\\\c)~~~~0,4^{-2}=6\dfrac{1}{4} \\\\d)~~~~12^{2}\cdot 7^{0}=144\\\\e)~~~~10^{-3} \cdot 10^{4}=10[/tex]
Szczegółowe wyjaśnienie:
Korzystamy ze wzorów:
[tex]a)~~~~(-6)^{3}\cdot \left(\dfrac{1}{3} \right)^{-2}=(-6)\cdot (-6)\cdot (-6)\cdot3^{2}=-216\cdot 3\cdot 3=-216\cdot 9=-1~944\\\\b)~~~~\left(3\dfrac{1}{4} \right)^{-2}=\left(\dfrac{3\cdot 4 +1}{4} \right)^{-2}=\left(\dfrac{13}{4} \right)^{-2}=\left(\dfrac{4}{13} \right)^{2}=\dfrac{4}{13}\cdot \dfrac{4}{13}=\dfrac{16}{169}\\\\[/tex]
[tex]c)~~~~0,4^{-2}=\left(\dfrac{4}{10} \right)^{-2}=\left(\dfrac{4\!\!\!\!\diagup^2}{10\!\!\!\!\!\diagup_5} \right)^{-2}=\left(\dfrac{2}{5} \right)^{-2}=\left(\dfrac{5}{2} \right)^{2}=\dfrac{5}{2} \cdot \dfrac{5}{2} =\dfrac{25}{4} =6\dfrac{1}{4} \\\\d)~~~~12^{2}\cdot 7^{0}=12\cdot 12\cdot 1=144\\\\e)~~~~10^{-3} \cdot 10^{4}=10^{-3+4}=10^{1}=10[/tex]
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Odpowiedź:
[tex]a)~~~~(-6)^{3}\cdot \left(\dfrac{1}{3} \right)^{-2}=-1~944\\\\b)~~~~\left(3\dfrac{1}{4} \right)^{-2}=\dfrac{16}{169}\\\\c)~~~~0,4^{-2}=6\dfrac{1}{4} \\\\d)~~~~12^{2}\cdot 7^{0}=144\\\\e)~~~~10^{-3} \cdot 10^{4}=10[/tex]
Szczegółowe wyjaśnienie:
Korzystamy ze wzorów:
Rozwiązanie:
[tex]a)~~~~(-6)^{3}\cdot \left(\dfrac{1}{3} \right)^{-2}=(-6)\cdot (-6)\cdot (-6)\cdot3^{2}=-216\cdot 3\cdot 3=-216\cdot 9=-1~944\\\\b)~~~~\left(3\dfrac{1}{4} \right)^{-2}=\left(\dfrac{3\cdot 4 +1}{4} \right)^{-2}=\left(\dfrac{13}{4} \right)^{-2}=\left(\dfrac{4}{13} \right)^{2}=\dfrac{4}{13}\cdot \dfrac{4}{13}=\dfrac{16}{169}\\\\[/tex]
[tex]c)~~~~0,4^{-2}=\left(\dfrac{4}{10} \right)^{-2}=\left(\dfrac{4\!\!\!\!\diagup^2}{10\!\!\!\!\!\diagup_5} \right)^{-2}=\left(\dfrac{2}{5} \right)^{-2}=\left(\dfrac{5}{2} \right)^{2}=\dfrac{5}{2} \cdot \dfrac{5}{2} =\dfrac{25}{4} =6\dfrac{1}{4} \\\\d)~~~~12^{2}\cdot 7^{0}=12\cdot 12\cdot 1=144\\\\e)~~~~10^{-3} \cdot 10^{4}=10^{-3+4}=10^{1}=10[/tex]