Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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