Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{4}{5} - \frac{3}{2} }= x^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ x^{7} }}=\frac{1}{\sqrt[10]{ x^{7} }}. \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x|}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{4} - \frac{4}{5} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
5. \(\dfrac{y^{2}}{y^{\frac{1}{3}}}\\= y^{ 2 - \frac{1}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{-5}{2}}}{y^{-1}}\\= y^{ \frac{-5}{2} - (-1) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
8. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{2}) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{5} - \frac{1}{4} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{4}{3} - (\frac{-1}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)