Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{4} - (\frac{-2}{3}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
2. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-5}{3} - \frac{4}{3} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
3. \(\dfrac{y^{-2}}{y^{\frac{5}{4}}}\\= y^{ -2 - \frac{5}{4} }= y^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ y^{13} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y }}=\frac{1}{|y^{3}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{4}|}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{5} - \frac{1}{3} }= y^{\frac{7}{15}}\\=\sqrt[15]{ y^{7} }\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{4}{5} - \frac{5}{3} }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{2}{3} - (\frac{-4}{5}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{6} - \frac{4}{5} }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{1}}\\= q^{ \frac{-2}{3} - 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{1}{6} - (\frac{-2}{5}) }= q^{\frac{17}{30}}\\=\sqrt[30]{ q^{17} }\\---------------\)