Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{2} - \frac{3}{5} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{3} - \frac{2}{3} }= a^{1}\\\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{5} - \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-2}{5} - \frac{5}{6} }= x^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[30]{ x^{7} }}=\frac{1}{|x|.\sqrt[30]{ x^{7} }} \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{3}{2} - \frac{2}{5} }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{1}{4}}}{x^{-1}}\\= x^{ \frac{1}{4} - (-1) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{4}{3} - \frac{1}{4} }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{5} - (\frac{-5}{4}) }= x^{\frac{29}{20}}\\=\sqrt[20]{ x^{29} }=|x|.\sqrt[20]{ x^{9} }\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{2}{5} - (\frac{-2}{3}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)