Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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