Kopertina e librit Matematika 9

Zgjidhja e ushtrimit 6

Zgjidhja e ushtrimit 6 të mësimit 3.2 në librin Matematika 9 nga shtëpia botuese Ideart Botime me autorë Patrick Kivlin, Sue Pemberton, Paul Winters.

Pyetja

Thjeshtoni shprehjet duke zbatuar vetitë e fuqive.

  1. x4×x3x5\dfrac{x^4\times x^3}{x^5}
  2. y8×y8y7\dfrac{y^8\times y^8}{y^7}
  3. x10x2×x4\dfrac{x^{10}}{x^2\times x^4}
  4. a4×a7a2×a3\dfrac{a^4\times a^7}{a^2\times a^3}
  5. 2x2×3x54x3\dfrac{2x^2\times 3x^5}{4x^3}
  6. 3y4×6y32y5\dfrac{3y^4\times6y^3}{2y^5}
  7. 8x92x3×2x4\dfrac{8x^9}{2x^3\times2x^4}
  8. 2a5×5a23a×4a4\dfrac{2a^5\times5a^2}{3a\times4a^4}

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Zgjidhja

  1. x4+3x5=x7:x5=x7−5=x2\dfrac{x^{4+3}}{x^5}=x^7:x^5=x^{7-5}=x^2
  2. y8+8y7=y16:y7=y16−7=y9\dfrac{y^{8+8}}{y^7}=y^{16}:y^7=y^{16-7}=y^9
  3. x10x2+4=x10:x6=x10−6=x4\dfrac{x^{10}}{x^{2+4}}=x^{10}:x^6=x^{10-6}=x^4
  4. a4+7a2+3=a11:a5=a11−5=a6\dfrac{a^{4+7}}{a^{2+3}}=a^{11}:a^5=a^{11-5}=a^6
  5. 2×3×x2+54x3=64×(x7:x3)=32×x7−3=3x42\dfrac{2\times3\times x^{2+5}}{4x^3}=\dfrac{6}{4}\times(x^7:x^3)=\dfrac{3}{2}\times x^{7-3}=\dfrac{3x^4}{2}
  6. 3×6×y4+32y5=182×(y7:y5)=9×y7−5=9y2\dfrac{3\times6\times y^{4+3}}{2y^5}=\dfrac{18}{2}\times(y^7:y^5)=9\times y^{7-5}=9y^2
  7. 8x92×2×x3+4=84×(x9:x7)=2×x9−7=2x2\dfrac{8x^9}{2\times2\times x^{3+4}}=\dfrac{8}{4}\times(x^9:x^7)=2\times x^{9-7}=2x^2
  8. 2×5×a5+23×4×a1+4=1012×(a7:a5)=56×a7−5=5a26\dfrac{2\times5\times a^{5+2}}{3\times4\times a^{1+4}}=\dfrac{10}{12}\times(a^7:a^5)=\dfrac{5}{6}\times a^{7-5}=\dfrac{5a^2}{6}