Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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