Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{3} - (\frac{-3}{5}) }= q^{\frac{14}{15}}\\=\sqrt[15]{ q^{14} }\\---------------\)
2. \(\dfrac{q^{-2}}{q^{\frac{-5}{4}}}\\= q^{ -2 - (\frac{-5}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{6} - \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-3}{2} - \frac{5}{2} }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-3}{4} - \frac{2}{5} }= q^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{3} }}=\frac{1}{|q|.\sqrt[20]{ q^{3} }} \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{5}{6}}}{y^{-2}}\\= y^{ \frac{5}{6} - (-2) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{a^{2}}{a^{\frac{-5}{3}}}\\= a^{ 2 - (\frac{-5}{3}) }= a^{\frac{11}{3}}\\=\sqrt[3]{ a^{11} }=a^{3}.\sqrt[3]{ a^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{3}{4} - (\frac{-3}{4}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{5}{2} - (\frac{-5}{3}) }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)