Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{4} - \frac{5}{3} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{y^{-2}}{y^{\frac{1}{5}}}\\= y^{ -2 - \frac{1}{5} }= y^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ y^{11} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y }}=\frac{1}{y^{2}.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{3}}\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{6} - \frac{5}{4} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{-1}}\\= x^{ \frac{5}{2} - (-1) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-2}{3} - (\frac{-3}{5}) }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)