Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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