Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{2} - (\frac{-1}{3}) }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{5}{4} - (\frac{-5}{3}) }= a^{\frac{35}{12}}\\=\sqrt[12]{ a^{35} }=|a^{2}|.\sqrt[12]{ a^{11} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{-1}}\\= q^{ \frac{1}{5} - (-1) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-4}{3}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
9. \(\dfrac{q^{\frac{-4}{3}}}{q^{-1}}\\= q^{ \frac{-4}{3} - (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{4}{5} - \frac{5}{6} }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
12. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)