Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{6} - (\frac{-4}{5}) }= y^{\frac{29}{30}}\\=\sqrt[30]{ y^{29} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{5}{6} - \frac{1}{3} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-3}{5}}}\\= a^{ 1 - (\frac{-3}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{4}}}{a^{-1}}\\= a^{ \frac{1}{4} - (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{3}{2}}}\\= x^{ 1 - \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
12. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{5} - (\frac{-1}{2}) }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)