Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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