Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{3} - \frac{1}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{2}{5} - (\frac{-4}{3}) }= y^{\frac{26}{15}}\\=\sqrt[15]{ y^{26} }=y.\sqrt[15]{ y^{11} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{4} - (\frac{-1}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-1}{5} - \frac{3}{5} }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-3}{5} - (\frac{-3}{4}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{6} - (\frac{-5}{4}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{3}{4} - (\frac{-5}{2}) }= x^{\frac{13}{4}}\\=\sqrt[4]{ x^{13} }=|x^{3}|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{6} - (\frac{-2}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{2}}\\= x^{ \frac{1}{2} - 2 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)