Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{2} - \frac{4}{5} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{2} - \frac{5}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{5} - \frac{5}{3} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{2}{3} - (\frac{-4}{5}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{-1}}\\= q^{ \frac{5}{6} - (-1) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{3}{4} - (\frac{-5}{2}) }= x^{\frac{13}{4}}\\=\sqrt[4]{ x^{13} }=|x^{3}|.\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{2} - \frac{2}{5} }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-4}{3} - \frac{5}{6} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)