Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{6} - \frac{2}{5} }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{3}{4} - (\frac{-5}{3}) }= y^{\frac{29}{12}}\\=\sqrt[12]{ y^{29} }=|y^{2}|.\sqrt[12]{ y^{5} }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-4}{5} - \frac{2}{5} }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-3}{5}}}\\= a^{ -1 - (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{3}{4} - (\frac{-1}{6}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{5}}}{a^{-1}}\\= a^{ \frac{-3}{5} - (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{3}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
9. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{5}{2} - (\frac{-1}{6}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}\\= x^{ \frac{5}{6} - \frac{1}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-5}{4} - (\frac{-3}{4}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)