Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{2}}}{a^{1}}\\= a^{ \frac{5}{2} - 1 }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-2}{3} - \frac{1}{4} }= q^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ q^{11} }}=\frac{1}{\sqrt[12]{ q^{11} }}. \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q|}\\---------------\)
3. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-4}{5} - \frac{3}{2} }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
5. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-5}{4} - \frac{1}{4} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-4}{3} - (\frac{-3}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-2}{5}) }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{4}{5}}}\\= x^{ 1 - \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{2} - (\frac{-4}{3}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{4}{3} - \frac{4}{5} }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)