Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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