Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{3} - \frac{1}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{4} - \frac{5}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-4}{3} - \frac{5}{2} }= x^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ x^{23} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{4}|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{2}}\\= y^{ \frac{-1}{2} - 2 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{5} - \frac{1}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{6}}}{a^{1}}\\= a^{ \frac{-5}{6} - 1 }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{2}{3} - (\frac{-1}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{3} - \frac{2}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{2} - (\frac{-1}{5}) }= q^{\frac{27}{10}}\\=\sqrt[10]{ q^{27} }=|q^{2}|.\sqrt[10]{ q^{7} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)