Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{2}}\\= y^{ -1 - 2 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{4}}}{a^{1}}\\= a^{ \frac{-5}{4} - 1 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-1}{6} - \frac{1}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{3}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{4}{3}}}\\= y^{ 1 - \frac{4}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
8. \(\dfrac{x^{2}}{x^{\frac{-5}{2}}}\\= x^{ 2 - (\frac{-5}{2}) }= x^{\frac{9}{2}}\\= \sqrt{ x^{9} } =|x^{4}|. \sqrt{ x } \\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{6} - (\frac{-5}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{1}}\\= a^{ \frac{-1}{4} - 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-3}{4} - (\frac{-1}{4}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)