Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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