Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{5}{3}}}\\= q^{ -1 - \frac{5}{3} }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{3}{2}}}\\= q^{ 1 - \frac{3}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{2} - \frac{5}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{2} - \frac{4}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{1}}\\= q^{ \frac{-2}{3} - 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{4} - \frac{2}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-5}{3} - \frac{1}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{2}{5} - (\frac{-3}{5}) }= y^{1}\\\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{3} - \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)