Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{4}}}{q^{-1}}\\= q^{ \frac{-1}{4} - (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{2} - \frac{4}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{5}{4} - \frac{4}{3} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{2} - \frac{5}{6} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{3}{5} - \frac{3}{2} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{2} - (\frac{-4}{5}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{-5}{3}}}\\= x^{ -2 - (\frac{-5}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{2} - \frac{1}{2} }= y^{2}\\\\---------------\)
9. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-5}{4} - (\frac{-1}{2}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{3} - (\frac{-3}{5}) }= q^{\frac{34}{15}}\\=\sqrt[15]{ q^{34} }=q^{2}.\sqrt[15]{ q^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{5}{3} - (\frac{-1}{5}) }= a^{\frac{28}{15}}\\=\sqrt[15]{ a^{28} }=a.\sqrt[15]{ a^{13} }\\---------------\)
12. \(\dfrac{y^{\frac{5}{6}}}{y^{-1}}\\= y^{ \frac{5}{6} - (-1) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)