Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{3}}}{q^{-1}}\\= q^{ \frac{1}{3} - (-1) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-4}{5} - (\frac{-5}{4}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-3}{4} - (\frac{-2}{3}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{1}{2} - \frac{3}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-5}{4} - \frac{1}{6} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{5} - \frac{5}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{2}{3} - (\frac{-3}{4}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{4} - \frac{1}{5} }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{5}}}{x^{-1}}\\= x^{ \frac{-2}{5} - (-1) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{2}}{a^{\frac{4}{3}}}\\= a^{ 2 - \frac{4}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{5}{2}}}\\= a^{ 1 - \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)