Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{2} - \frac{2}{5} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
2. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{4}{5} - (\frac{-1}{3}) }= x^{\frac{17}{15}}\\=\sqrt[15]{ x^{17} }=x.\sqrt[15]{ x^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{3}{5} - \frac{5}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{4}{5} - (\frac{-3}{2}) }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{2} - \frac{5}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{3}{4} - (\frac{-4}{5}) }= a^{\frac{31}{20}}\\=\sqrt[20]{ a^{31} }=|a|.\sqrt[20]{ a^{11} }\\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{1}}\\= q^{ \frac{-2}{3} - 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{3} - (\frac{-4}{5}) }= a^{\frac{22}{15}}\\=\sqrt[15]{ a^{22} }=a.\sqrt[15]{ a^{7} }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{2}}\\= a^{ \frac{-2}{3} - 2 }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{2} - (\frac{-3}{5}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)