Odpowiedź:
√[4⁻² * (1/16)³] = √[(1/4)² * (1/16)³] = √[1/16 * (1/16)³] = √(1/6) * √(1/16)² * √(1/16) = 1/4 * 1/16 * 1/4 = 1/16 * 1/16 = (1/16)² = 1/256
√[4⁻² * (1/16)³] = √[(1/4)² * (1/16)³] = √[(1/6) * (1/16)³] = √(1/16)¹⁺³ = √(1/16)⁴ =
= √(1/16)² * √(1/16)² = 1/16 * 1/16 = 1/256
√[4⁻² * (1/16)³] = √[(2²)⁻² * (1/2)¹²] = √[(2⁻⁴) * 2⁻¹²] = √(2⁻⁴⁻¹²) = √2⁻¹⁶ =
= √(1/2)¹⁶ =
= √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² =
= 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/256
[tex]\huge\boxed{\sqrt{4^{-2}\times\left(\frac{1}{16}\right)^{3}} =\left(\frac{1}{2}\right)^{8} = \frac{1}{256}}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z własności potęgowania:
[tex](a^{m})^{n} = a^{m\cdot n}\\\\a^{m}\cdot a^{n}=a^{m+n}\\\\a^{-n} = \frac{1}{a^{n}}[/tex]
[tex]\sqrt{4^{-2}\times(\frac{1}{16})^{3}} = \sqrt{(\frac{1}{4})^{2}\times(\frac{1}{16})^{3}} = \sqrt{((\frac{1}{2})^{2})^{2}\times((\frac{1}{2})^{4})^{3}} = \sqrt{(\frac{1}{2})^{4}\times(\frac{1}{2})^{12}}=\\\\\\=\sqrt{(\frac{1}{2})^{16}} = ((\frac{1}{2})^{16})^\frac{1}{2}} = (\frac{1}{2})^{8} = \frac{1}{2^{8}} = \frac{1}{256}[/tex]
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Odpowiedź:
√[4⁻² * (1/16)³] = √[(1/4)² * (1/16)³] = √[1/16 * (1/16)³] = √(1/6) * √(1/16)² * √(1/16) = 1/4 * 1/16 * 1/4 = 1/16 * 1/16 = (1/16)² = 1/256
√[4⁻² * (1/16)³] = √[(1/4)² * (1/16)³] = √[(1/6) * (1/16)³] = √(1/16)¹⁺³ = √(1/16)⁴ =
= √(1/16)² * √(1/16)² = 1/16 * 1/16 = 1/256
√[4⁻² * (1/16)³] = √[(2²)⁻² * (1/2)¹²] = √[(2⁻⁴) * 2⁻¹²] = √(2⁻⁴⁻¹²) = √2⁻¹⁶ =
= √(1/2)¹⁶ =
= √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² * √(1/2)² =
= 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/256
A) (1/2)^3/4
B) 2^3
C) [4√(1/2)]^5
D) 2^2/3
Odpowiedź:
[tex]\huge\boxed{\sqrt{4^{-2}\times\left(\frac{1}{16}\right)^{3}} =\left(\frac{1}{2}\right)^{8} = \frac{1}{256}}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z własności potęgowania:
[tex](a^{m})^{n} = a^{m\cdot n}\\\\a^{m}\cdot a^{n}=a^{m+n}\\\\a^{-n} = \frac{1}{a^{n}}[/tex]
[tex]\sqrt{4^{-2}\times(\frac{1}{16})^{3}} = \sqrt{(\frac{1}{4})^{2}\times(\frac{1}{16})^{3}} = \sqrt{((\frac{1}{2})^{2})^{2}\times((\frac{1}{2})^{4})^{3}} = \sqrt{(\frac{1}{2})^{4}\times(\frac{1}{2})^{12}}=\\\\\\=\sqrt{(\frac{1}{2})^{16}} = ((\frac{1}{2})^{16})^\frac{1}{2}} = (\frac{1}{2})^{8} = \frac{1}{2^{8}} = \frac{1}{256}[/tex]