Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-2}}{y^{\frac{5}{3}}}\\= y^{ -2 - \frac{5}{3} }= y^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ y^{11} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{4}}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{1}{6}}}\\= q^{ -1 - \frac{1}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{5}{6}}}\\= q^{ 1 - \frac{5}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{2}}\\= q^{ -1 - 2 }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{4} - \frac{2}{3} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{5}}}{q^{-2}}\\= q^{ \frac{-2}{5} - (-2) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{3} - (\frac{-2}{3}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{5} - \frac{1}{6} }= y^{\frac{-11}{30}}\\=\frac{1}{\sqrt[30]{ y^{11} }}=\frac{1}{\sqrt[30]{ y^{11} }}. \color{purple}{\frac{\sqrt[30]{ y^{19} }}{\sqrt[30]{ y^{19} }}} \\=\frac{\sqrt[30]{ y^{19} }}{|y|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{3} - (\frac{-2}{3}) }= a^{1}\\\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)