Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-2}{3} - \frac{2}{5} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{6}) }= a^{0}\\=1\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{2} - (\frac{-3}{2}) }= a^{2}\\\\---------------\)
5. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{5} - \frac{1}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-5}{6} - \frac{5}{4} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{5}{4} - (\frac{-4}{5}) }= a^{\frac{41}{20}}\\=\sqrt[20]{ a^{41} }=|a^{2}|.\sqrt[20]{ a }\\---------------\)
9. \(\dfrac{a^{-2}}{a^{\frac{-1}{2}}}\\= a^{ -2 - (\frac{-1}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
11. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{2} - \frac{5}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)