Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{5} - \frac{2}{3} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{5}{4} - \frac{3}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{2} - (\frac{-3}{5}) }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{6}}}{a^{1}}\\= a^{ \frac{-1}{6} - 1 }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{1}{6}}}\\= q^{ 1 - \frac{1}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{6}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{1}{6} - (\frac{-3}{2}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-4}{3} - (\frac{-1}{3}) }= a^{-1}\\=\frac{1}{a}\\---------------\)