Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{2} - \frac{1}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{2}{3} - (\frac{-1}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-4}{3} - \frac{3}{4} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-1}{5}}}\\= a^{ 1 - (\frac{-1}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-3}{4} - \frac{1}{6} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{1}}\\= x^{ \frac{4}{5} - 1 }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
10. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{3} - (\frac{-1}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{4}) }= x^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{4}{5} - \frac{5}{2} }= a^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{7} }}=\frac{1}{|a|.\sqrt[10]{ a^{7} }} \color{purple}{\frac{\sqrt[10]{ a^{3} }}{\sqrt[10]{ a^{3} }}} \\=\frac{\sqrt[10]{ a^{3} }}{|a^{2}|}\\---------------\)