Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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