Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{2} - \frac{5}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{4} - (\frac{-1}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-1}{4}}}\\= x^{ -1 - (\frac{-1}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-5}{6} - \frac{1}{5} }= q^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ q^{31} }}\\=\frac{1}{|q|.\sqrt[30]{ q }}=\frac{1}{|q|.\sqrt[30]{ q }} \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{2} - (\frac{-1}{3}) }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-2}{3} - \frac{3}{4} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{5}}}{a^{1}}\\= a^{ \frac{-3}{5} - 1 }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)