Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{-1}{3}}}\\= q^{ -2 - (\frac{-1}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
6. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{3} - (\frac{-1}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-4}{3}) }= a^{1}\\\\---------------\)
9. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{4}{5} - (\frac{-1}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-1}{4} - \frac{5}{3} }= x^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{11} }}=\frac{1}{|x|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-5}{2} - \frac{1}{3} }= a^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ a^{17} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{3}|}\\---------------\)