Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{5} - \frac{1}{2} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{3} - (\frac{-3}{5}) }= y^{\frac{34}{15}}\\=\sqrt[15]{ y^{34} }=y^{2}.\sqrt[15]{ y^{4} }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{2}{5} - (\frac{-3}{5}) }= q^{1}\\\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{6}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{2}{5} - (\frac{-1}{3}) }= a^{\frac{11}{15}}\\=\sqrt[15]{ a^{11} }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{1}}\\= q^{ \frac{3}{2} - 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{4} - \frac{1}{4} }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{1}{3}}}\\= q^{ -1 - \frac{1}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-1}{6}}}\\= a^{ 1 - (\frac{-1}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\dfrac{x^{-2}}{x^{\frac{-1}{5}}}\\= x^{ -2 - (\frac{-1}{5}) }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{4} - \frac{4}{3} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)