Odpowiedź:
[tex]\huge\boxed{\sqrt[3]{x}\cdot x^{\frac{2}{3}}:x^{2} = x^{-1}}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z praw potęgowania:
[tex]a^{1} = a\\\\a^{\frac{1}{n}} = \sqrt[n]{a}\\\\a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
[tex]\sqrt[3]{x}\cdot x^{\frac{2}{3}}:x^{2}} = x^{\frac{1}{3}}\cdot x^{\frac{2}{3}}:x^{2} = x^{\frac{1}{3}+\frac{2}{3}}:x^{2} = x^{\frac{3}{3}}:x^{2} = x^{1}:x^{2} = x^{1-2} =\boxed{ x^{-1}}[/tex]
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Odpowiedź:
[tex]\huge\boxed{\sqrt[3]{x}\cdot x^{\frac{2}{3}}:x^{2} = x^{-1}}[/tex]
Szczegółowe wyjaśnienie:
Działania na potęgach
Korzystamy z praw potęgowania:
[tex]a^{1} = a\\\\a^{\frac{1}{n}} = \sqrt[n]{a}\\\\a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
[tex]\sqrt[3]{x}\cdot x^{\frac{2}{3}}:x^{2}} = x^{\frac{1}{3}}\cdot x^{\frac{2}{3}}:x^{2} = x^{\frac{1}{3}+\frac{2}{3}}:x^{2} = x^{\frac{3}{3}}:x^{2} = x^{1}:x^{2} = x^{1-2} =\boxed{ x^{-1}}[/tex]