Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{5}{4}}}\\= q^{ 1 - \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{3} - \frac{5}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{2}{3} - \frac{1}{4} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{6}}}{x^{1}}\\= x^{ \frac{1}{6} - 1 }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{2} - (\frac{-2}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{4}{3} - (\frac{-2}{3}) }= y^{2}\\\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{5} - (\frac{-1}{2}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
9. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-5}{3} - \frac{2}{5} }= q^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ q^{31} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q }}=\frac{1}{q^{2}.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{3}}\\---------------\)
10. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{5}{6} - \frac{5}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)