Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-3}{4} - (\frac{-3}{5}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{2}{3} - (\frac{-1}{3}) }= y^{1}\\\\---------------\)
3. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-5}{3} - \frac{3}{5} }= x^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ x^{34} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{3}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{3} - \frac{5}{2} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{5}{4}}}\\= a^{ -1 - \frac{5}{4} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{4} - (\frac{-1}{3}) }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{2} - (\frac{-5}{2}) }= y^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-4}{3} - (\frac{-3}{4}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{3} - \frac{2}{5} }= x^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ x^{31} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x }}=\frac{1}{x^{2}.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{3}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{5} - \frac{5}{4} }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)