Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-4}{5} - (\frac{-3}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-3}{2}) }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-1}{2}}}\\= y^{ -1 - (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{2}{5} - (\frac{-1}{4}) }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{3}{4}}}{q^{-2}}\\= q^{ \frac{3}{4} - (-2) }= q^{\frac{11}{4}}\\=\sqrt[4]{ q^{11} }=|q^{2}|.\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{3} - (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{2} - (\frac{-4}{3}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)