Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{2} - (\frac{-2}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{q^{-2}}{q^{\frac{3}{2}}}\\= q^{ -2 - \frac{3}{2} }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{5} - \frac{1}{2} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\\= y^{ -1 - \frac{1}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{4}{5} - \frac{5}{4} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{-1}}\\= q^{ \frac{1}{2} - (-1) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{2} - \frac{1}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-5}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{3}) }= y^{0}\\=1\\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{3} - (\frac{-1}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)