Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{1}{3} - (\frac{-3}{4}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{6}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-2}{3}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{3}{4} - \frac{1}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{-4}{3}}}{q^{-2}}\\= q^{ \frac{-4}{3} - (-2) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
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. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-3}{2} - (\frac{-5}{6}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{-1}}\\= x^{ \frac{-3}{4} - (-1) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{2}{3} - \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)