Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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