Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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