Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
2. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{6} - (\frac{-1}{2}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-5}{3} - \frac{5}{3} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{3}{4} - \frac{5}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-4}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
10. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-3}{5} - \frac{3}{4} }= y^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ y^{27} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{7} }}=\frac{1}{|y|.\sqrt[20]{ y^{7} }} \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{4} - (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{-1}}\\= y^{ \frac{1}{5} - (-1) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)