Odpowiedź:
ćw. 1
[tex]3 \times {3}^{4} \times ( {3}^{2} {)}^{3} = 3 \times {3}^{4} \times {3}^{6} = {3}^{1 + 4 + 6} = {3}^{11} [/tex]
A.
[tex] {12}^{5} \div {a}^{5} = {2}^{10} \\ \frac{ {12}^{5} }{ {a}^{5} } = 1024 \: \: \: \: | \times {a}^{5} \\ {12}^{5} = 1024 {a}^{5} \\ {a}^{5} = \frac{ {12}^{5} }{1024} \\ {a}^{5} = {3}^{5} \\ a = 3[/tex]
ćw. 2
[tex] \sqrt{2} \times ( - \sqrt{8} ) = - \sqrt{16} \\ - \sqrt{16} > - \sqrt{18} [/tex]
F.
[tex] \sqrt{2} + \sqrt{32} - \sqrt{8} - \sqrt{18} = \sqrt{2} + 4 \sqrt{2} - 2 \sqrt{2} - 3 \sqrt{2} = 5 \sqrt{2} - 5 \sqrt{2} = 0[/tex]
P.
ćw. 3
[tex]a) - {3}^{2} - ( - 5 {)}^{3} = - 9 - ( - 125) = - 9 + 125 = 116[/tex]
[tex]b) \sqrt[3]{ - 15 \frac{5}{8} } + \frac{12}{ \sqrt{64} } = \sqrt[3]{ - \frac{125}{8} } + \frac{12}{8} = - \frac{5}{2} + \frac{12}{8} = - \frac{20}{8} + \frac{12}{8} = - \frac{8}{8} = - 1[/tex]
[tex]c)(3 \frac{1}{3} {)}^{4} \div ( \frac{5}{6} {)}^{4} = (\frac{10}{3} {)}^{4} \div ( \frac{5}{6} {)}^{4} = ( \frac{10}{3} \times \frac{6}{5} {)}^{4} = (2 \times 2 {)}^{4} = {4}^{4} = 256[/tex]
[tex]d) \sqrt{10 \frac{2}{3} } \times \sqrt{1.5} = \sqrt{ \frac{32}{3} } \times \sqrt{ \frac{15}{10} } = \sqrt{ \frac{32}{3} } \times \sqrt{ \frac{3}{2} } = \sqrt{ \frac{32}{2} } = \sqrt{16} = 4[/tex]
