Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{2}}}\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{3}}}\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{5}}}\)
4. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\)
5. \(\dfrac{x^{-1}}{x^{\frac{-5}{4}}}\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{4}}}\)
7. \(\dfrac{y^{\frac{-1}{4}}}{y^{1}}\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\)
9. \(\dfrac{q^{-1}}{q^{\frac{-1}{5}}}\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{1}}\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{3}}}\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{2}}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{3} - \frac{1}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-1}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-2}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-5}{4}}}\\= x^{ -1 - (\frac{-5}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{4}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{4}}}{y^{1}}\\= y^{ \frac{-1}{4} - 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{-1}{5}}}\\= q^{ -1 - (\frac{-1}{5}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{1}}\\= a^{ \frac{-2}{5} - 1 }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{2} - (\frac{-5}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{3} - \frac{1}{2} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)