Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{-5}{6}}}\\= x^{ 1 - (\frac{-5}{6}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
2. \(\dfrac{x^{-2}}{x^{\frac{5}{2}}}\\= x^{ -2 - \frac{5}{2} }= x^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ x^{9} } }\\=\frac{1}{|x^{4}|. \sqrt{ x } }=\frac{1}{|x^{4}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{5}|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{3} - \frac{5}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{2}) }= q^{\frac{19}{10}}\\=\sqrt[10]{ q^{19} }=|q|.\sqrt[10]{ q^{9} }\\---------------\)
5. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{-5}{3}}}\\= q^{ 1 - (\frac{-5}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{6} - \frac{5}{4} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{4}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{2}{3} - (\frac{-1}{3}) }= a^{1}\\\\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)
12. \(\dfrac{q^{2}}{q^{\frac{5}{4}}}\\= q^{ 2 - \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)