Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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