Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{4} - (\frac{-4}{5}) }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
4. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-2}{3}) }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-5}{6} - \frac{1}{4} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-4}{5} - \frac{1}{3} }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{3}{2}}}\\= a^{ \frac{3}{5} - \frac{3}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-2}{3} - \frac{5}{4} }= x^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{11} }}=\frac{1}{|x|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{5} - (\frac{-5}{6}) }= x^{\frac{43}{30}}\\=\sqrt[30]{ x^{43} }=|x|.\sqrt[30]{ x^{13} }\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{3}{2} - \frac{2}{5} }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)