Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{4} - \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{3}}}{y^{-1}}\\= y^{ \frac{-5}{3} - (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-3}{5} - (\frac{-5}{6}) }= y^{\frac{7}{30}}\\=\sqrt[30]{ y^{7} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{3} - (\frac{-4}{5}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-4}{3} - \frac{1}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{y^{2}}{y^{\frac{2}{3}}}\\= y^{ 2 - \frac{2}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{6}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-4}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{5}{4}}}\\= x^{ 1 - \frac{5}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{4} - \frac{4}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{4} - (\frac{-1}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)