Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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