Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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