Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{2} - \frac{4}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{3}{4} - \frac{5}{3} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{2} - \frac{2}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{2} - (\frac{-3}{5}) }= y^{\frac{11}{10}}\\=\sqrt[10]{ y^{11} }=|y|.\sqrt[10]{ y }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{2}}\\= a^{ \frac{-1}{2} - 2 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{3} - \frac{2}{3} }= a^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{1}}\\= q^{ \frac{5}{3} - 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-2}{3}) }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)