Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{5} - \frac{1}{3} }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
2. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-2}{5} - \frac{4}{3} }= q^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ q^{26} }}\\=\frac{1}{q.\sqrt[15]{ q^{11} }}=\frac{1}{q.\sqrt[15]{ q^{11} }} \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{1}{4}}}\\= a^{ 1 - \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{1}{6}}}\\= a^{ -1 - \frac{1}{6} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{3}{5} - (\frac{-1}{3}) }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{2} - \frac{5}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{4}}}{q^{-2}}\\= q^{ \frac{1}{4} - (-2) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{6} - (\frac{-3}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-2}{3} - \frac{5}{4} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)