Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{3}{4} - (\frac{-5}{4}) }= y^{2}\\\\---------------\)
2. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{6}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-3}{4} - \frac{3}{2} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{3} - \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{6} - \frac{5}{6} }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-5}{4} - \frac{5}{3} }= q^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ q^{35} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q^{11} }}=\frac{1}{|q^{2}|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-4}{3} - \frac{4}{5} }= y^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ y^{32} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{3}}\\---------------\)
11. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{3} - \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{2} - \frac{2}{3} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)