Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{4}{5} - (\frac{-1}{2}) }= a^{\frac{13}{10}}\\=\sqrt[10]{ a^{13} }=|a|.\sqrt[10]{ a^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{2} - \frac{5}{6} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{4}{3}}}\\= a^{ -1 - \frac{4}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-3}{4} - (\frac{-5}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
7. \(\dfrac{q^{-2}}{q^{\frac{-4}{3}}}\\= q^{ -2 - (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{6}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-2}{5} - \frac{1}{2} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
11. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{5} - (\frac{-5}{2}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
12. \(\dfrac{y^{\frac{3}{4}}}{y^{1}}\\= y^{ \frac{3}{4} - 1 }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)