Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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