Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-3}{2} - \frac{4}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-5}{2} - \frac{4}{5} }= q^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ q^{33} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{4}|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{2} - \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{2}{5} - (\frac{-5}{6}) }= a^{\frac{37}{30}}\\=\sqrt[30]{ a^{37} }=|a|.\sqrt[30]{ a^{7} }\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-2}{3} - \frac{4}{5} }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(\dfrac{a^{\frac{1}{4}}}{a^{2}}\\= a^{ \frac{1}{4} - 2 }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{2}{3} - (\frac{-3}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{2} - (\frac{-5}{6}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)