Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{4} - \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{2} - \frac{5}{6} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{3}{4} - (\frac{-5}{4}) }= q^{2}\\\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-5}{6}}}\\= q^{ -1 - (\frac{-5}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{5}{3} - (\frac{-2}{5}) }= y^{\frac{31}{15}}\\=\sqrt[15]{ y^{31} }=y^{2}.\sqrt[15]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-5}{2}) }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{3} - (\frac{-1}{3}) }= q^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{5}{3} - (\frac{-5}{4}) }= a^{\frac{35}{12}}\\=\sqrt[12]{ a^{35} }=|a^{2}|.\sqrt[12]{ a^{11} }\\---------------\)
11. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{4}{5} - (\frac{-1}{6}) }= a^{\frac{29}{30}}\\=\sqrt[30]{ a^{29} }\\---------------\)