Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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