Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{2} - \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{6} - \frac{1}{5} }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-3}{5} - \frac{5}{6} }= a^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ a^{43} }}\\=\frac{1}{|a|.\sqrt[30]{ a^{13} }}=\frac{1}{|a|.\sqrt[30]{ a^{13} }} \color{purple}{\frac{\sqrt[30]{ a^{17} }}{\sqrt[30]{ a^{17} }}} \\=\frac{\sqrt[30]{ a^{17} }}{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{2}}}{q^{1}}\\= q^{ \frac{3}{2} - 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{5}{4}}}\\= y^{ -1 - \frac{5}{4} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{1}{5}}}\\= x^{ -1 - \frac{1}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{4}{3}}}{a^{-2}}\\= a^{ \frac{4}{3} - (-2) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{3} - \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{2}{3} - (\frac{-5}{4}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)