Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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