Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{2}) }= y^{1}\\\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{-1}}\\= x^{ \frac{1}{2} - (-1) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{-4}{5}}}\\= y^{ -1 - (\frac{-4}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{2} - (\frac{-1}{6}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{3} - \frac{5}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{4}{3} - (\frac{-3}{2}) }= a^{\frac{17}{6}}\\=\sqrt[6]{ a^{17} }=|a^{2}|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{5}{2}}}\\= y^{ 1 - \frac{5}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{2} - (\frac{-1}{2}) }= x^{3}\\\\---------------\)
10. \(\dfrac{x^{\frac{5}{3}}}{x^{1}}\\= x^{ \frac{5}{3} - 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{6}}}{y^{2}}\\= y^{ \frac{1}{6} - 2 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)