Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{2} - \frac{5}{6} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{3}{2} - (\frac{-1}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{5} - \frac{1}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-2}{5}}}\\= x^{ 1 - (\frac{-2}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{5}}}{a^{-1}}\\= a^{ \frac{1}{5} - (-1) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{1}{2} - (\frac{-1}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{6} - (\frac{-3}{5}) }= y^{\frac{13}{30}}\\=\sqrt[30]{ y^{13} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
11. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)