Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{6}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{4}}}{y^{1}}\\= y^{ \frac{-5}{4} - 1 }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-5}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{3} - \frac{4}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-5}{4} - \frac{4}{5} }= y^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ y^{41} }}\\=\frac{1}{|y^{2}|.\sqrt[20]{ y }}=\frac{1}{|y^{2}|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-4}{5} - \frac{3}{2} }= x^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ x^{23} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{4}}}{x^{2}}\\= x^{ \frac{-5}{4} - 2 }= x^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ x^{13} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x }}=\frac{1}{|x^{3}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{4}|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
10. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{3} - \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)