Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-4}{3} - (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
3. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)
4. \(\dfrac{y^{1}}{y^{2}}\\= y^{ 1 - 2 }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{5} - (\frac{-5}{4}) }= a^{\frac{29}{20}}\\=\sqrt[20]{ a^{29} }=|a|.\sqrt[20]{ a^{9} }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-5}{6} - \frac{3}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{3} - (\frac{-2}{5}) }= a^{\frac{31}{15}}\\=\sqrt[15]{ a^{31} }=a^{2}.\sqrt[15]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)