Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{4} - (\frac{-2}{3}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{4}}}{y^{1}}\\= y^{ \frac{1}{4} - 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-5}{2} - (\frac{-3}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{5}{4} - (\frac{-3}{5}) }= x^{\frac{37}{20}}\\=\sqrt[20]{ x^{37} }=|x|.\sqrt[20]{ x^{17} }\\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{2} - \frac{5}{4} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{5} - (\frac{-1}{2}) }= y^{\frac{11}{10}}\\=\sqrt[10]{ y^{11} }=|y|.\sqrt[10]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{2}{3} - (\frac{-1}{5}) }= x^{\frac{13}{15}}\\=\sqrt[15]{ x^{13} }\\---------------\)
11. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{4} - \frac{1}{2} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)