Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{3}{5} - (\frac{-4}{3}) }= y^{\frac{29}{15}}\\=\sqrt[15]{ y^{29} }=y.\sqrt[15]{ y^{14} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{2} - \frac{3}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{5} - \frac{1}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{4} - \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-2}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{2}{5}}}{q^{-2}}\\= q^{ \frac{2}{5} - (-2) }= q^{\frac{12}{5}}\\=\sqrt[5]{ q^{12} }=q^{2}.\sqrt[5]{ q^{2} }\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-4}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{4} - (\frac{-3}{2}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)