Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{6} - \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{6} - \frac{2}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{5}{4} - (\frac{-1}{6}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-5}{4} - \frac{3}{5} }= x^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{17} }}=\frac{1}{|x|.\sqrt[20]{ x^{17} }} \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{5}{2} - (\frac{-5}{3}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{3}{5} - (\frac{-1}{6}) }= a^{\frac{23}{30}}\\=\sqrt[30]{ a^{23} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{6} - \frac{5}{6} }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-3}{4} - (\frac{-2}{3}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-3}{4}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{3}{2}}}\\= x^{ 1 - \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{5}{6} - (\frac{-3}{2}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)