Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{6} - \frac{1}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{6}) }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-2}{3} - \frac{5}{2} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{2} - \frac{4}{3} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
6. \(\dfrac{x^{-2}}{x^{\frac{4}{5}}}\\= x^{ -2 - \frac{4}{5} }= x^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ x^{14} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{3}}\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{5}{3}}}\\= x^{ 1 - \frac{5}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{6} - (\frac{-3}{5}) }= q^{\frac{23}{30}}\\=\sqrt[30]{ q^{23} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{3} - \frac{1}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{5} - (\frac{-4}{3}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{4} - \frac{5}{3} }= a^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ a^{35} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{2}{3} - \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)