Odpowiedź:
[tex]\huge\boxed {~~c)~~\left (\sqrt{\dfrac{1}{3} } \right)^{2}\cdot \sqrt{\dfrac{1}{25} } =\dfrac{1}{15} ~~}[/tex]
[tex]\huge\boxed {~~d)~~\sqrt[3]{\dfrac{1}{125} } -\left (\sqrt[3]{\dfrac{1}{5} } \right)^{3}=0~~}[/tex]
Szczegółowe wyjaśnienie:
Pamiętamy o kolejności wykonywanych działań
Korzystamy ze wzoru:
Obliczamy :
[tex]c)~~\left (\sqrt{\dfrac{1}{3} } \right)^{2}\cdot \sqrt{\dfrac{1}{25} } =\left (\dfrac{1}{3} \right)^{2\cdot \frac{1}{2} }\cdot \sqrt{\left(\dfrac{1}{5} \right)^{2}} =\dfrac{1}{3} \cdot =\left (\dfrac{1}{5} \right)^{2\cdot \frac{1}{2} }=\dfrac{1}{3} \cdot \dfrac{1}{5} =\dfrac{1}{15}[/tex]
[tex]d)~~\sqrt[3]{\dfrac{1}{125} } -\left (\sqrt[3]{\dfrac{1}{5} } \right)^{3}=\sqrt[3]{\left(\dfrac{1}{5} \right)^{3}} -\left (\dfrac{1}{5} \right)^{3\cdot \frac{1}{3} }=\left (\dfrac{1}{5} \right)^{3\cdot \frac{1}{3} }-\dfrac{1}{5} =\dfrac{1}{5} -\dfrac{1}{5} =0[/tex]
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Odpowiedź:
[tex]\huge\boxed {~~c)~~\left (\sqrt{\dfrac{1}{3} } \right)^{2}\cdot \sqrt{\dfrac{1}{25} } =\dfrac{1}{15} ~~}[/tex]
[tex]\huge\boxed {~~d)~~\sqrt[3]{\dfrac{1}{125} } -\left (\sqrt[3]{\dfrac{1}{5} } \right)^{3}=0~~}[/tex]
Szczegółowe wyjaśnienie:
Pamiętamy o kolejności wykonywanych działań
Korzystamy ze wzoru:
Obliczamy :
[tex]c)~~\left (\sqrt{\dfrac{1}{3} } \right)^{2}\cdot \sqrt{\dfrac{1}{25} } =\left (\dfrac{1}{3} \right)^{2\cdot \frac{1}{2} }\cdot \sqrt{\left(\dfrac{1}{5} \right)^{2}} =\dfrac{1}{3} \cdot =\left (\dfrac{1}{5} \right)^{2\cdot \frac{1}{2} }=\dfrac{1}{3} \cdot \dfrac{1}{5} =\dfrac{1}{15}[/tex]
[tex]d)~~\sqrt[3]{\dfrac{1}{125} } -\left (\sqrt[3]{\dfrac{1}{5} } \right)^{3}=\sqrt[3]{\left(\dfrac{1}{5} \right)^{3}} -\left (\dfrac{1}{5} \right)^{3\cdot \frac{1}{3} }=\left (\dfrac{1}{5} \right)^{3\cdot \frac{1}{3} }-\dfrac{1}{5} =\dfrac{1}{5} -\dfrac{1}{5} =0[/tex]