Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{2} - \frac{5}{4} }= y^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ y^{11} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{5} - \frac{1}{2} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
5. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{4} - (\frac{-2}{3}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{5}{6}}}\\= y^{ 1 - \frac{5}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-5}{3} - \frac{1}{5} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{5} - (\frac{-1}{4}) }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{3} - (\frac{-4}{3}) }= q^{2}\\\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{1}}\\= a^{ \frac{-1}{5} - 1 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{2}}\\= x^{ -1 - 2 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)