Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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