Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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