Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{2} - (\frac{-3}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-2}{3} - \frac{3}{4} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-2}{3} - \frac{3}{2} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{2} - (\frac{-1}{2}) }= y^{2}\\\\---------------\)
9. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-4}{3} - (\frac{-1}{4}) }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{5} - (\frac{-4}{3}) }= x^{\frac{23}{15}}\\=\sqrt[15]{ x^{23} }=x.\sqrt[15]{ x^{8} }\\---------------\)
11. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{2}{5} - \frac{1}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{2} - (\frac{-1}{2}) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)