Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-4}{3}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{2} - \frac{1}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
6. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{4} - (\frac{-4}{3}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{3}{2} - (\frac{-1}{5}) }= a^{\frac{17}{10}}\\=\sqrt[10]{ a^{17} }=|a|.\sqrt[10]{ a^{7} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{5}) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-1}{2} - \frac{3}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{3} - (\frac{-5}{4}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{2} - \frac{4}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-5}{3} - (\frac{-3}{4}) }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)