Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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