Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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