Kopertina e librit Matematika 10 - 11: Pjesa II

Zgjidhja e ushtrimit 8

Zgjidhja e ushtrimit 8 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

Njehsoni shprehjet e mëposhtme.

  1. 251225^{\frac{1}{2}}
  2. 25−1225^{-\frac{1}{2}}
  3. 25025^0
  4. 253225^{\frac{3}{2}}
  5. 25−125^{-1}
  6. 25−3225^{-\frac{3}{2}}
  7. 163216^{\frac{3}{2}}
  8. 272327^{\frac{2}{3}}
  9. 4−324^{-\frac{3}{2}}
  10. 81−0.2581^{-0.25}
  11. 125−23125^{-\frac{2}{3}}
  12. 100−72100^{-\frac{7}{2}}
  13. 4324^{\frac{3}{2}}
  14. 8238^{\frac{2}{3}}
  15. 9529^{\frac{5}{2}}
  16. 100−12100^{-\frac{1}{2}}
  17. 16−3216^{-\frac{3}{2}}
  18. 1000231000^{\frac{2}{3}}
  19. 400−12400^{-\frac{1}{2}}
  20. 16932169^{\frac{3}{2}}
  21. 4−324^{-\frac{3}{2}}

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Zgjidhja

  1. 25=5\sqrt{25} = 5
  2. 125=15\dfrac{1}{\sqrt{25}} = \dfrac{1}{5}
  3. 1
  4. 253=252×25=25×5=105\sqrt{25^3} = \sqrt{25^2} \times \sqrt{25} = 25 \times 5 = 105
  5. 125\dfrac{1}{25}
  6. 1253=1252×25=125×5=1105\dfrac{1}{\sqrt{25^3}} = \dfrac{1}{\sqrt{25^2}\times\sqrt{25}} = \dfrac{1}{25 \times 5} = \dfrac{1}{105}
  7. 42×32=42×32=43=644^{2 \times \frac{3}{2}} = 4^{\cancel{2} \times \frac{3}{\cancel{2}}} = 4^3 = 64
  8. 33×23=33×23=32=93^{3 \times \frac{2}{3}} = 3^{\cancel{3} \times \frac{2}{\cancel{3}}} = 3^2 = 9
  9. 1432=143=142×4=14×2=18\dfrac{1}{4^{\frac{3}{2}}} = \dfrac{1}{\sqrt{4^3}} = \dfrac{1}{\sqrt{4^2} \times \sqrt{4}} = \dfrac{1}{4 \times 2} = \dfrac{1}{8}
  10. 81−14=34×(−14)=34×(−14)=3−1=1381^{-\frac{1}{4}} = 3^{4 \times (-\frac{1}{4})} = 3^{\cancel{4} \times (-\frac{1}{\cancel{4}})} = 3^{-1} = \dfrac{1}{3}
  11. 53×(−23)=53×(−23)=5−2=1255^{3 \times (-\frac{2}{3})} = 5^{\cancel{3} \times ({-\frac{2}{\cancel{3}}})} = 5^{-2} = \dfrac{1}{25}
  12. 102×(−72)=102×(−72)=10−7=110710^{2 \times (-\frac{7}{2})} = 10^{\cancel{2} \times (-\frac{7}{\cancel{2}})} = 10^{-7} = \dfrac{1}{10^7}
  13. 22×32=22×32=23=82^{2 \times \frac{3}{2}} = 2^{\cancel{2} \times \frac{3}{\cancel{2}}} = 2^3 = 8
  14. 23×23=23×23=22=42^{3 \times \frac{2}{3}} = 2^{\cancel{3} \times \frac{2}{\cancel{3}}} = 2^2 = 4
  15. 932+22=932×9=32×32×9=32×32×9=33×9=2439^{{\frac{3}{2}} + \frac{2}{2}} = 9^{\frac{3}{2}} \times 9 = 3^{2 \times \frac{3}{2}} \times 9 = 3^{\cancel{2} \times \frac{3}{\cancel{2}}} \times 9 = 3^3 \times 9 = 243
  16. 102×(−12)=102×(−12)=10−1=11010^{2 \times (-\frac{1}{2})} = 10^{\cancel{2} \times {(-\frac{1}{\cancel{2}})}} = 10^{-1} = \dfrac{1}{10}
  17. 42×(−32)=42×(−32)=4−3=143=1644^{2 \times (-\frac{3}{2})} = 4^{\cancel{2} \times (-\frac{3}{\cancel{2}})} = 4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}
  18. 103×23=103×23=102=10010^{3 \times \frac{2}{3}} = 10^{\cancel{3} \times \frac{2}{\cancel{3}}} = 10^2 = 100
  19. 1400=120\dfrac{1}{\sqrt{400}} = \dfrac{1}{20}
  20. 132×32=132×32=133=291713^{2 \times \frac{3}{2}} = 13^{\cancel{2} \times \frac{3}{\cancel{2}}} = 13^3 = 2917
  21. 22×(−32)=22×(−32)=2−3=123=182^{2 \times (-\frac{3}{2})} = 2^{\cancel{2} \times (-\frac{3}{\cancel{2}})} = 2^{-3} = \dfrac{1}{2^3} = \dfrac{1}{8}