Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{-1}}\\= y^{ \frac{-2}{3} - (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{5} - \frac{1}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{1}}\\= y^{ \frac{-1}{3} - 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{4} - \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{1}{2} - \frac{5}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\\= x^{ 1 - (\frac{-1}{6}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{3} - (\frac{-1}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{2}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{6}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)