Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-4}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-3}{2} - \frac{1}{6} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{5}}}\\= y^{ \frac{5}{3} - \frac{1}{5} }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
5. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{2} - \frac{2}{3} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{-1}}\\= y^{ \frac{5}{4} - (-1) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
10. \(\dfrac{q^{-2}}{q^{1}}\\= q^{ -2 - 1 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{2} - \frac{5}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{3}{4}}}{x^{-1}}\\= x^{ \frac{3}{4} - (-1) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)