Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{2} - (\frac{-1}{2}) }= a^{2}\\\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{3} - \frac{3}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{2}{3} - (\frac{-5}{6}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{-1}{5}}}\\= y^{ 1 - (\frac{-1}{5}) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{1}{5}}}\\= a^{ \frac{3}{2} - \frac{1}{5} }= a^{\frac{13}{10}}\\=\sqrt[10]{ a^{13} }=|a|.\sqrt[10]{ a^{3} }\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{3}{5}}}\\= x^{ -2 - \frac{3}{5} }= x^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ x^{13} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{3} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{3}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{6} - \frac{5}{2} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{3} - \frac{2}{3} }= q^{0}\\=1\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{1}}\\= y^{ \frac{-1}{3} - 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-4}{5} - \frac{5}{4} }= q^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ q^{41} }}\\=\frac{1}{|q^{2}|.\sqrt[20]{ q }}=\frac{1}{|q^{2}|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{3}|}\\---------------\)