Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{2}}\\= q^{ -1 - 2 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{1}}\\= q^{ \frac{-3}{5} - 1 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{3}{2} - (\frac{-1}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
4. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{6} - (\frac{-5}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-3}{4}}}\\= x^{ -1 - (\frac{-3}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{5} - (\frac{-5}{2}) }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{1}{5} - (\frac{-3}{4}) }= q^{\frac{19}{20}}\\=\sqrt[20]{ q^{19} }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-4}{5}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{2} - (\frac{-2}{3}) }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{2}{3} - (\frac{-4}{5}) }= x^{\frac{22}{15}}\\=\sqrt[15]{ x^{22} }=x.\sqrt[15]{ x^{7} }\\---------------\)