Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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