Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{3} - \frac{1}{2} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{3}}}{a^{2}}\\= a^{ \frac{-5}{3} - 2 }= a^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ a^{11} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{4}}\\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{5} - \frac{3}{4} }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-4}{5} - \frac{5}{3} }= q^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ q^{37} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{3}}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{6}}}{q^{-1}}\\= q^{ \frac{-1}{6} - (-1) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-1}{3} - \frac{1}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{6} - \frac{2}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{2}{5} - (\frac{-5}{2}) }= q^{\frac{29}{10}}\\=\sqrt[10]{ q^{29} }=|q^{2}|.\sqrt[10]{ q^{9} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{4} - \frac{3}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{2} - \frac{5}{6} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)