Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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