Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-5}{3} - \frac{3}{2} }= a^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ a^{19} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a }}=\frac{1}{|a^{3}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{4}|}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{2}}\\= x^{ -1 - 2 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{-1}}\\= x^{ \frac{1}{2} - (-1) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-2}{3} - \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
7. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{4}{5} - \frac{4}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
8. \(\dfrac{x^{\frac{5}{6}}}{x^{-1}}\\= x^{ \frac{5}{6} - (-1) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{q^{-2}}{q^{-1}}\\= q^{ -2 - (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\dfrac{y^{\frac{-3}{5}}}{y^{-1}}\\= y^{ \frac{-3}{5} - (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{3} - \frac{5}{4} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)