Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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