Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{5} - \frac{5}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{5}{2} - (\frac{-1}{3}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{5}) }= q^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ q^{7} }}=\frac{1}{\sqrt[15]{ q^{7} }}. \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-2}{3} - \frac{5}{6} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-5}{3}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{2}{5} - (\frac{-5}{4}) }= q^{\frac{33}{20}}\\=\sqrt[20]{ q^{33} }=|q|.\sqrt[20]{ q^{13} }\\---------------\)
8. \(\dfrac{x^{2}}{x^{-1}}\\= x^{ 2 - (-1) }= x^{3}\\\\---------------\)
9. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{4}{3} - \frac{3}{4} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{3}{4} - (\frac{-3}{2}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-3}{4}}}\\= q^{ -1 - (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)