Odpowiedź:
[tex]\huge\boxed{\frac{16^{3}:0,5}{4^{2}\cdot2^{3}} = 2^{6} = 64}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z praw potęgowania:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\a^{-n} = \frac{1}{a^{n}}[/tex]
[tex]\frac{16^{3}:0,5}{4^{2}\cdot2^{3}} = \frac{(2^{4})^{3}:\frac{1}{2}}{(2^{2})^{2}\cdot2^{3}} = \frac{2^{4\cdot3}:2^{-1}}{2^{2\cdot2}\cdot2^{3}} = \frac{2^{12}:2^{-1}}{2^{4}\cdot2^{3}} = \frac{2^{12-(-1)}}{2^{4+3}} = \frac{2^{13}}{2^{7}} = 2^{13-7} = 2^{6} = 64[/tex]
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Verified answer
Odpowiedź:
[tex]\huge\boxed{\frac{16^{3}:0,5}{4^{2}\cdot2^{3}} = 2^{6} = 64}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z praw potęgowania:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\a^{-n} = \frac{1}{a^{n}}[/tex]
[tex]\frac{16^{3}:0,5}{4^{2}\cdot2^{3}} = \frac{(2^{4})^{3}:\frac{1}{2}}{(2^{2})^{2}\cdot2^{3}} = \frac{2^{4\cdot3}:2^{-1}}{2^{2\cdot2}\cdot2^{3}} = \frac{2^{12}:2^{-1}}{2^{4}\cdot2^{3}} = \frac{2^{12-(-1)}}{2^{4+3}} = \frac{2^{13}}{2^{7}} = 2^{13-7} = 2^{6} = 64[/tex]