Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{3}}}{y^{-1}}\\= y^{ \frac{-5}{3} - (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\dfrac{a^{\frac{-3}{2}}}{a^{1}}\\= a^{ \frac{-3}{2} - 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{1}}\\= q^{ \frac{-5}{4} - 1 }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{5}{3} - \frac{1}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{2} - \frac{1}{2} }= q^{1}\\\\---------------\)
7. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{3}{5} - (\frac{-1}{2}) }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{5} - \frac{1}{2} }= x^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[10]{ x }}=\frac{1}{|x|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-3}{4} - (\frac{-4}{5}) }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{3} - (\frac{-3}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{3}) }= a^{0}\\=1\\---------------\)
12. \(\dfrac{x^{2}}{x^{\frac{5}{3}}}\\= x^{ 2 - \frac{5}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)