Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{2} - \frac{3}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{2} - (\frac{-5}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{5} - \frac{2}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{2} - \frac{4}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{q^{-2}}{q^{\frac{2}{3}}}\\= q^{ -2 - \frac{2}{3} }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{3}{5}}}\\= x^{ -1 - \frac{3}{5} }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{5}{2}}}\\= a^{ 1 - \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-4}{5}) }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-3}{4} - (\frac{-5}{3}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)