Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-5}{6} - (\frac{-5}{4}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{2} - \frac{5}{3} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{3}{4} - (\frac{-3}{2}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{3}{5}}}\\= a^{ -1 - \frac{3}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-4}{5}}}{x^{1}}\\= x^{ \frac{-4}{5} - 1 }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{1}{6}}}\\= x^{ -1 - \frac{1}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{a^{2}}{a^{\frac{-5}{4}}}\\= a^{ 2 - (\frac{-5}{4}) }= a^{\frac{13}{4}}\\=\sqrt[4]{ a^{13} }=|a^{3}|.\sqrt[4]{ a }\\---------------\)