Răspuns:
24. a) [tex]\frac{3}{4}+(\frac{1}{2}) ^{2} =\frac{3}{4}+\frac{1}{4} =1[/tex]
b) [tex]5-(\frac{5}{6})^{2}=5-\frac{25}{36} =\frac{180-25}{36}=\frac{155}{36}[/tex]
c) [tex]\frac{6}{7}-(\frac{1}{10})^{3} =\frac{6}{7} -\frac{1}{1000} =\frac{6000-7}{7000}=\frac{5993}{7000}[/tex]
25. a) x²⁰·x³⁴=x²⁰⁺³⁴=x⁵⁴=[tex](\frac{5}{6})^{54}[/tex]
b) x³⁴:x²⁰=x⁴³⁻²⁰=x¹⁴=[tex](\frac{5}{6})^{14}[/tex]
c) (x²⁰)³⁴=x²⁰*³⁴=x⁶⁸⁰=[tex](\frac{5}{6})^{680}[/tex]
26. a) [tex](\frac{3}{7}) ^{2} =\frac{9}{47}[/tex]
b) [tex](\frac{5}{9}) ^{0} =1[/tex]
c) [tex](\frac{2}{5}) ^{2} *10-\frac{7}{5} =\frac{40}{25} -\frac{7}{5}=\frac{40-35}{25}=\frac{5}{25} =\frac{1}{5}[/tex]
27. a) [tex](\frac{3}{2}) ^{2} =\frac{2)9}{4}=\frac{18}{8}[/tex] [tex](\frac{3}{2}) ^{3} =\frac{27}{8}[/tex] [tex]\frac{18}{8} <\frac{27}{8}[/tex] ⇒ [tex](\frac{3}{2}) ^{2} <(\frac{3}{2}) ^{3}[/tex]
b) [tex](\frac{1}{10}) ^{2} =\frac{10)1}{100}=\frac{10}{1000}[/tex] [tex](\frac{1}{10}) ^{3} =\frac{1}{1000}[/tex] [tex]\frac{10}{1000} >\frac{1}{1000}[/tex] ⇒ [tex](\frac{1}{10}) ^{2} >(\frac{1}{10}) ^{3}[/tex]
c) [tex]\frac{5}{5} =1[/tex] 1²=1 1³=1 1=1 ⇒ 1²=1³
Explicație pas cu pas:
