Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
2. \(\dfrac{y^{\frac{-4}{3}}}{y^{-2}}\\= y^{ \frac{-4}{3} - (-2) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
5. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{5} - \frac{4}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{6} - \frac{2}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{4}{3}}}\\= a^{ -1 - \frac{4}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{5} - \frac{3}{4} }= x^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{11} }}=\frac{1}{|x|.\sqrt[20]{ x^{11} }} \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{4} - (\frac{-1}{6}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
10. \(\dfrac{a^{\frac{5}{4}}}{a^{-1}}\\= a^{ \frac{5}{4} - (-1) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{3}{4} - (\frac{-4}{5}) }= x^{\frac{31}{20}}\\=\sqrt[20]{ x^{31} }=|x|.\sqrt[20]{ x^{11} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)