Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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