Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{3} - (\frac{-5}{2}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{4} - \frac{1}{4} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{3}{5}}}\\= x^{ \frac{5}{6} - \frac{3}{5} }= x^{\frac{7}{30}}\\=\sqrt[30]{ x^{7} }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-5}{2}}}\\= q^{ -1 - (\frac{-5}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{3} - \frac{1}{3} }= x^{0}\\=1\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{5}{6} - (\frac{-4}{3}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{3} - \frac{3}{4} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-4}{5} - (\frac{-3}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
12. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-4}{3} - (\frac{-5}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)