Odpowiedź:
1.
a) <-4,5>.
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-4. 5
-4 ≤ x ≤ 5
b). (-2,0>
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-2. 0
-2 < x ≤ 0
c). (-∞,4)
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4
-∞ < x < 4
2.
a)
AuB=<-4,8)
AnB=(-2,5>
A\B=<-4,-2>
B\A=(5,8)
b)
AuB=<-10, 5)
AnB=(-4,-2>
A\B=<-10,-4>
B\A=(-2,5)
3.
[tex]a) \: \: {5}^{ - 4} = ( \frac{1}{5} {)}^{4} = \frac{1}{625}[/tex]
[tex]b) \: \: ( \frac{3}{4} {)}^{ - 4} = ( \frac{4}{3} {)}^{4} = \frac{256}{81} = 3 \frac{13}{81} [/tex]
[tex]c) \: \: (1 \frac{2}{3} {)}^{3} = ( \frac{5}{3} {)}^{3} = \frac{125}{27} = 4 \frac{17}{27} [/tex]
[tex]d) \: \: (5 \frac{3}{4} {)}^{ - 2} = ( \frac{23}{4} {)}^{ - 2} = ( \frac{4}{23 }{)}^{2} = \frac{16}{529} [/tex]
[tex]f) \: \: 3 - {2}^{ - 2} \times ( \frac{3}{7} {)}^{0} = 3 - \frac{1}{4} \times 1 = 2 \frac{3}{4} [/tex]
4.
[tex]a) \: \: {9}^{ - 4} \times ( \frac{1}{3} {)}^{ - 4} = (9 \times \frac{1}{3} {)}^{ - 4} = {3}^{ - 4} = (\frac{1}{3} {)}^{4} [/tex]
[tex]b) \: \: \frac{( {3}^{4} {)}^{5} }{ {3}^{5} \times {3}^{6} } = \frac{ {3}^{20} }{ {3}^{11} } = {3}^{9} [/tex]
[tex]c) \: \: \frac{ ({7}^{4} {)}^{6} }{ {7}^{2} \times {49}^{6} } = \frac{ {7}^{24} }{ {7}^{2} \times ( {7}^{2} {)}^{6} } = \frac{ {7}^{24} }{ {7}^{14} } = {7}^{10} [/tex]
6.
[tex]a) \: \: a - b = \frac{2}{15} - \frac{3}{10} = \frac{4}{30} - \frac{9}{30} = - \frac{5}{30} = - \frac{1}{6} [/tex]
[tex]b) \: \: a \times b = \frac{2}{15} \times \frac{3}{10} = \frac{1}{25} [/tex]
[tex]c) \: \: \frac{a}{b} = \frac{ \frac{2}{15} }{ \frac{3}{10} } = \frac{2}{15} \times \frac{10}{3} = \frac{4}{9} [/tex]
7
[tex]a) \: \: \sqrt{128} = \sqrt{64 \times 2} = 8 \sqrt{2} [/tex]
[tex]b) \: \: \sqrt{50} = \sqrt{25 \times 2} = 5 \sqrt{2} [/tex]
[tex]c) \: \: \sqrt[3]{320} = \sqrt[3]{64 \times 5} = 4 \sqrt[3]{5} [/tex]
[tex]d) \: \: \sqrt[3]{1024} = \sqrt[3]{512 \times 2} = 8 \sqrt[3]{2} [/tex]
8.
[tex]a) \: \: (2 {x}^{2} + 5x - 3) + ( - {x}^{2} + 7x - 9) = {x}^{2} + 12x - 12[/tex]
[tex]b) \: \: (4m - 2n + 1) - (7 m+ 3n - 12) = - 3m - 5n + 13[/tex]
[tex]c) \: \: ( - 3 {x}^{3} y)( - 4x) = 12 {x}^{5} y[/tex]
[tex]d) \: \: (2x + 3)(4x - 5) = {8x}^{2} - 10x + 12x - 15 = {8x}^{2} - 2x - 15[/tex]
