Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{5} - \frac{1}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{1}{4}}}\\= a^{ 1 - \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{2} - (\frac{-1}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{5}{3} - (\frac{-5}{2}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{2} - (\frac{-3}{5}) }= y^{\frac{11}{10}}\\=\sqrt[10]{ y^{11} }=|y|.\sqrt[10]{ y }\\---------------\)
6. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{4} - \frac{2}{3} }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{5} - \frac{2}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-3}{2} - (\frac{-1}{6}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{2}{3} - (\frac{-3}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{5}{2} - \frac{3}{5} }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{3} - \frac{1}{4} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)