Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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