Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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