Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-3}{4} - (\frac{-3}{5}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{2}{3} - (\frac{-2}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-4}{5}}}{a^{1}}\\= a^{ \frac{-4}{5} - 1 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{3}) }= q^{1}\\\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{2}{3} - \frac{3}{5} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-5}{3} - \frac{5}{4} }= a^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ a^{35} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{3}|}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{4}{5} - (\frac{-4}{3}) }= y^{\frac{32}{15}}\\=\sqrt[15]{ y^{32} }=y^{2}.\sqrt[15]{ y^{2} }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-5}{6}}}\\= q^{ -1 - (\frac{-5}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)