Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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