Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-2}{3} - \frac{1}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{2} - \frac{1}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{4}{3}}}{q^{1}}\\= q^{ \frac{4}{3} - 1 }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{-4}{5}}}{a^{-1}}\\= a^{ \frac{-4}{5} - (-1) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{-2}{5}}}\\= q^{ 1 - (\frac{-2}{5}) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{1}}\\= q^{ \frac{-1}{6} - 1 }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{-1}}\\= y^{ \frac{-1}{4} - (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{3}{4} - \frac{1}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{5} - \frac{5}{3} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-1}{6}}}\\= q^{ -1 - (\frac{-1}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)