Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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