Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-1}{3} - \frac{1}{5} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
3. \(\dfrac{y^{-2}}{y^{-1}}\\= y^{ -2 - (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{4} - \frac{5}{3} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{6} - \frac{1}{2} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-4}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
9. \(\dfrac{x^{\frac{-3}{4}}}{x^{-1}}\\= x^{ \frac{-3}{4} - (-1) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{x^{\frac{3}{5}}}{x^{-1}}\\= x^{ \frac{3}{5} - (-1) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{5} - (\frac{-4}{3}) }= a^{\frac{29}{15}}\\=\sqrt[15]{ a^{29} }=a.\sqrt[15]{ a^{14} }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)