Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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