Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{4}) }= x^{\frac{7}{20}}\\=\sqrt[20]{ x^{7} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{1}{2} - (\frac{-1}{5}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
3. \(\dfrac{y^{\frac{2}{5}}}{y^{-2}}\\= y^{ \frac{2}{5} - (-2) }= y^{\frac{12}{5}}\\=\sqrt[5]{ y^{12} }=y^{2}.\sqrt[5]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-4}{5} - \frac{2}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{3} - (\frac{-1}{3}) }= y^{2}\\\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{3}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
10. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{4} - (\frac{-4}{3}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
11. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{3} - \frac{1}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)