Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
2. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{3} - (\frac{-4}{5}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
3. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{2} - \frac{1}{5} }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{4} - \frac{2}{5} }= x^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ x^{33} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{13} }}=\frac{1}{|x|.\sqrt[20]{ x^{13} }} \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{3} - \frac{4}{5} }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{3}{4} - \frac{5}{3} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-1}{6}}}\\= a^{ -1 - (\frac{-1}{6}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{2}{3} - \frac{5}{2} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{6} - (\frac{-5}{4}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-5}{3}) }= q^{0}\\=1\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)