Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{2} - \frac{2}{5} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-1}{2}}}\\= y^{ -1 - (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-4}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{1}{5} - \frac{1}{5} }= a^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{3} - (\frac{-5}{6}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{3}{2} - \frac{5}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
7. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{5} - (\frac{-1}{2}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{3} - \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{5} - \frac{5}{2} }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-5}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{5} - \frac{1}{2} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)