Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{3} - (\frac{-5}{6}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{3} - \frac{1}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
4. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{5}{6} - (\frac{-1}{4}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{3} - \frac{1}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{5}{4}}}\\= x^{ 1 - \frac{5}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{4} - \frac{2}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{5}{3} - \frac{5}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{-1}}\\= a^{ \frac{5}{6} - (-1) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{5}}}{q^{2}}\\= q^{ \frac{-1}{5} - 2 }= q^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ q^{11} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q }}=\frac{1}{q^{2}.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{3}}\\---------------\)