Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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