Kopertina e librit Matematika 10 - 11: Pjesa II

Zgjidhja e ushtrimit 11

Zgjidhja e ushtrimit 11 të mësimit 5.1A në librin Matematika 10 - 11: Pjesa II nga shtëpia botuese Botime Pegi me autorë Steve Fearnley, June Haighton, Steve Lomax, Peter Mullarkey, James Nicholson dhe Matt Nixon.

Pyetja

Thjeshtoni shprehjet e mëposhtme.

  1. (512)2(5^{\frac{1}{2}})^2
  2. (513)2(5^{\frac{1}{3}})^2
  3. (52)13(5^2)^{\frac{1}{3}}
  4. (513)12(5^{\frac{1}{3}})^{\frac{1}{2}}
  5. (5−2)2(5^{-2})^2
  6. (53)−2(5^3)^{-2}
  7. (5−1)−3(5^{-1})^{-3}
  8. (5−54)−2(5^{-\frac{5}{4}})^{-2}
  9. (5−2)34(5^{-2})^{\frac{3}{4}}
  10. (5−25)32(5^{-\frac{2}{5}})^{\frac{3}{2}}
  11. (565)−13(5^{\frac{6}{5}})^{-\frac{1}{3}}
  12. (5−23)54(5^{-\frac{2}{3}})^{\frac{5}{4}}

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Zgjidhja

  1. 512×2=55^{\frac{1}{\cancel{2}} \times \cancel{2}} = 5
  2. 513×2=5235^{\frac{1}{3} \times 2} = 5^{\frac{2}{3}}
  3. 52×13=5235^{2 \times \frac{1}{3}} = 5^{\frac{2}{3}}
  4. 513×12=5165^{\frac{1}{3} \times \frac{1}{2}} = 5^{\frac{1}{6}}
  5. 5(−2)×2=5−45^{(-2) \times 2} = 5^{-4}
  6. 53×(−2)=5−65^{3 \times (-2)} = 5^{-6}
  7. 5(−1)×(−3)=535^{(-1) \times (-3)} = 5^3
  8. 5(−54)×(−2)=5525^{(-\frac{5}{\cancel{4}}) \times (\cancel{-2})} = 5^{\frac{5}{2}}
  9. 5(−2)×34=5−325^{(\cancel{-2}) \times \frac{3}{\cancel{4}}} = 5^{-\frac{3}{2}}
  10. 5(−25)×32=5−355^{(-\frac{\cancel{2}}{5}) \times \frac{3}{\cancel{2}}} = 5^{-\frac{3}{5}}
  11. 565×(−13)=5−255^{\frac{\cancel{6}}{5} \times (-\frac{1}{\cancel{3}})} = 5^{-\frac{2}{5}}
  12. 5−23×54=5−565^{-\frac{\cancel{2}}{3} \times {\frac{5}{\cancel{4}}}} = 5^{-\frac{5}{6}}