Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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