Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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