Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{5} - \frac{1}{3} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{3} - (\frac{-1}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{5}{2}}}\\= y^{ 1 - \frac{5}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{3} - (\frac{-4}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{6}) }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{2}}\\= y^{ \frac{-1}{5} - 2 }= y^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ y^{11} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y }}=\frac{1}{y^{2}.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{3}}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{6} - (\frac{-5}{6}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{x^{-2}}{x^{\frac{2}{3}}}\\= x^{ -2 - \frac{2}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{4}}}{x^{-1}}\\= x^{ \frac{-1}{4} - (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{5} - \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{4}}}{y^{1}}\\= y^{ \frac{-3}{4} - 1 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)