Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{-1}{2}}}\\= q^{ -2 - (\frac{-1}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{5}{4} - \frac{3}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-1}{4}}}\\= a^{ 1 - (\frac{-1}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{5} - \frac{5}{6} }= y^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ y^{31} }}\\=\frac{1}{|y|.\sqrt[30]{ y }}=\frac{1}{|y|.\sqrt[30]{ y }} \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{3}{4} - \frac{5}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{3}{4} - \frac{3}{4} }= a^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-5}{3} - (\frac{-5}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)