Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{3}{2} - \frac{4}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{6} - (\frac{-1}{2}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{5}{2} - \frac{3}{2} }= q^{1}\\\\---------------\)
4. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{5} - \frac{5}{3} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{a^{2}}{a^{\frac{-1}{5}}}\\= a^{ 2 - (\frac{-1}{5}) }= a^{\frac{11}{5}}\\=\sqrt[5]{ a^{11} }=a^{2}.\sqrt[5]{ a }\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{2}{3} - (\frac{-5}{4}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-3}{4} - \frac{1}{5} }= q^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ q^{19} }}=\frac{1}{\sqrt[20]{ q^{19} }}. \color{purple}{\frac{\sqrt[20]{ q }}{\sqrt[20]{ q }}} \\=\frac{\sqrt[20]{ q }}{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{-1}}\\= x^{ \frac{1}{5} - (-1) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{3}{2} - (\frac{-3}{2}) }= q^{3}\\\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{4} - \frac{2}{3} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{-1}}\\= x^{ \frac{1}{2} - (-1) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)