Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-2}{3} - \frac{1}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{6} - (\frac{-1}{5}) }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-5}{2} - \frac{3}{4} }= a^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ a^{13} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a }}=\frac{1}{|a^{3}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{4}|}\\---------------\)
4. \(\dfrac{q^{1}}{q^{-2}}\\= q^{ 1 - (-2) }= q^{3}\\\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{2}{3} - \frac{5}{6} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
7. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{5}{4} - \frac{1}{6} }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{4} - \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{6}}}{y^{-1}}\\= y^{ \frac{1}{6} - (-1) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{5} - \frac{1}{2} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)