Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{4}{5} - (\frac{-3}{5}) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{6} - (\frac{-5}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{3}{4}}}\\= a^{ 1 - \frac{3}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{5} - (\frac{-1}{3}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{3} - (\frac{-5}{4}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
7. \(\dfrac{x^{\frac{-4}{3}}}{x^{-1}}\\= x^{ \frac{-4}{3} - (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{-1}}\\= q^{ \frac{-3}{4} - (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{2}}\\= y^{ \frac{-1}{3} - 2 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-4}{3} - \frac{3}{4} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)