Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{-1}}\\= y^{ \frac{-4}{3} - (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{2} - \frac{4}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-4}{3}}}\\= q^{ 1 - (\frac{-4}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-5}{4} - \frac{5}{6} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{3} - \frac{3}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{2} - \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{3}{2} - \frac{3}{2} }= q^{0}\\=1\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{6} - \frac{5}{4} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{4}{5}}}\\= y^{ 1 - \frac{4}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)