Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{3} - \frac{5}{2} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{5}{4}}}{a^{-1}}\\= a^{ \frac{5}{4} - (-1) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{3} - \frac{1}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{2}}\\= q^{ \frac{1}{3} - 2 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{4}{5} - (\frac{-5}{3}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
8. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{4}{3} - (\frac{-2}{3}) }= q^{2}\\\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{4}{5} - (\frac{-5}{2}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-1}{6}}}\\= q^{ -1 - (\frac{-1}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{4} - (\frac{-2}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{3} - \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)