Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{6} - (\frac{-1}{2}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{3}{2} - (\frac{-3}{4}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{x^{\frac{1}{3}}}{x^{2}}\\= x^{ \frac{1}{3} - 2 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{3}{2} - \frac{5}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
5. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{2} - \frac{2}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-4}{3} - (\frac{-5}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-2}{3}}}\\= x^{ -1 - (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{4} - \frac{4}{3} }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-2}{3}) }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-3}{2} - \frac{5}{4} }= a^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ a^{11} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{3}|}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)