Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-2}}{x^{\frac{5}{2}}}\\= x^{ -2 - \frac{5}{2} }= x^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ x^{9} } }\\=\frac{1}{|x^{4}|. \sqrt{ x } }=\frac{1}{|x^{4}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{5}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{5} - \frac{2}{3} }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
3. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-3}{4} - \frac{4}{5} }= x^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{11} }}=\frac{1}{|x|.\sqrt[20]{ x^{11} }} \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{2} - (\frac{-5}{6}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{-2}}\\= y^{ \frac{-4}{5} - (-2) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-4}{3}}}\\= y^{ 1 - (\frac{-4}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{5} - \frac{2}{3} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{3}{4}}}\\= x^{ 1 - \frac{3}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-5}{2} - \frac{3}{5} }= q^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ q^{31} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q }}=\frac{1}{|q^{3}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{4}|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{6} - (\frac{-2}{3}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{5}{4} - (\frac{-3}{5}) }= x^{\frac{37}{20}}\\=\sqrt[20]{ x^{37} }=|x|.\sqrt[20]{ x^{17} }\\---------------\)