Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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