Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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