Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{2} - (\frac{-5}{6}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{6} - \frac{4}{5} }= x^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ x^{19} }}=\frac{1}{\sqrt[30]{ x^{19} }}. \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{5} - \frac{1}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{5}{3} - (\frac{-1}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{3}{5}}}\\= q^{ 1 - \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{4} - \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)