Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-1}{2} - \frac{5}{3} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{4} - \frac{5}{3} }= x^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ x^{35} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }}=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{6} - (\frac{-1}{2}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-2}{3}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
5. \(\dfrac{q^{-2}}{q^{2}}\\= q^{ -2 - 2 }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{-2}}\\= a^{ \frac{2}{3} - (-2) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{-1}{5}}}\\= a^{ -1 - (\frac{-1}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{-1}{6}}}\\= y^{ -1 - (\frac{-1}{6}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{5} - \frac{5}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)