Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{4}{3} - \frac{5}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{4} - \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{1}{6}}}\\= x^{ -1 - \frac{1}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{3} - \frac{1}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{6} - \frac{5}{4} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-4}{3} - \frac{5}{3} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{5} - (\frac{-2}{3}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{1}{5} - (\frac{-3}{4}) }= q^{\frac{19}{20}}\\=\sqrt[20]{ q^{19} }\\---------------\)