Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{5}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
3. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{6} - (\frac{-5}{2}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-3}{5} - (\frac{-3}{4}) }= a^{\frac{3}{20}}\\=\sqrt[20]{ a^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{5} - (\frac{-5}{3}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{5} - (\frac{-1}{2}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{4} - (\frac{-4}{5}) }= a^{\frac{11}{20}}\\=\sqrt[20]{ a^{11} }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{4} - \frac{4}{3} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)