Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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