Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-4}{5} - (\frac{-5}{6}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-3}{5} - \frac{2}{3} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-5}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
6. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{3}{4} - (\frac{-5}{3}) }= y^{\frac{29}{12}}\\=\sqrt[12]{ y^{29} }=|y^{2}|.\sqrt[12]{ y^{5} }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{3}{2}}}\\= x^{ 1 - \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{3}{2} - (\frac{-2}{5}) }= q^{\frac{19}{10}}\\=\sqrt[10]{ q^{19} }=|q|.\sqrt[10]{ q^{9} }\\---------------\)
10. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{3} - (\frac{-1}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{3} - \frac{5}{3} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)