Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{2} - (\frac{-5}{6}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
3. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{4}{3} - (\frac{-4}{5}) }= x^{\frac{32}{15}}\\=\sqrt[15]{ x^{32} }=x^{2}.\sqrt[15]{ x^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{2}}\\= x^{ \frac{-5}{2} - 2 }= x^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ x^{9} } }\\=\frac{1}{|x^{4}|. \sqrt{ x } }=\frac{1}{|x^{4}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{5}|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-1}{6} - \frac{2}{5} }= x^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ x^{17} }}=\frac{1}{\sqrt[30]{ x^{17} }}. \color{purple}{\frac{\sqrt[30]{ x^{13} }}{\sqrt[30]{ x^{13} }}} \\=\frac{\sqrt[30]{ x^{13} }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{5} - (\frac{-2}{3}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
9. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{-5}{4}}}\\= q^{ 1 - (\frac{-5}{4}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{3} - (\frac{-1}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)