Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{-4}{5}}}{a^{-1}}\\= a^{ \frac{-4}{5} - (-1) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{1}}\\= x^{ \frac{-5}{4} - 1 }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-4}{5} - \frac{1}{3} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
9. \(\dfrac{y^{2}}{y^{1}}\\= y^{ 2 - 1 }= y^{1}\\\\---------------\)
10. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{6} - \frac{1}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{4} - \frac{2}{3} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)