Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{6}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{2}{3} - \frac{2}{3} }= y^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-4}{3}}}{a^{-2}}\\= a^{ \frac{-4}{3} - (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{6} - (\frac{-1}{2}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-3}{2} - (\frac{-1}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{2}}\\= x^{ \frac{4}{5} - 2 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{2}{3}}}{q^{2}}\\= q^{ \frac{2}{3} - 2 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-3}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{4} - (\frac{-2}{3}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)