Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{3}{4} - (\frac{-2}{5}) }= a^{\frac{23}{20}}\\=\sqrt[20]{ a^{23} }=|a|.\sqrt[20]{ a^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-2}{5}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
3. \(\dfrac{y^{2}}{y^{\frac{-5}{6}}}\\= y^{ 2 - (\frac{-5}{6}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-1}{6} - \frac{1}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{2} - \frac{1}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-5}{4}) }= x^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{6} - \frac{2}{5} }= q^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ q^{7} }}=\frac{1}{\sqrt[30]{ q^{7} }}. \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q|}\\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{4}{5}}}\\= x^{ \frac{5}{6} - \frac{4}{5} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
12. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{1}{4} - (\frac{-2}{5}) }= q^{\frac{13}{20}}\\=\sqrt[20]{ q^{13} }\\---------------\)