Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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