Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
2. \(\dfrac{x^{2}}{x^{\frac{3}{5}}}\\= x^{ 2 - \frac{3}{5} }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-2}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{4} - \frac{1}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{2}}}{q^{1}}\\= q^{ \frac{3}{2} - 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{5} - (\frac{-4}{3}) }= x^{\frac{29}{15}}\\=\sqrt[15]{ x^{29} }=x.\sqrt[15]{ x^{14} }\\---------------\)
8. \(\dfrac{a^{\frac{5}{3}}}{a^{-1}}\\= a^{ \frac{5}{3} - (-1) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-2}{5} - (\frac{-3}{4}) }= y^{\frac{7}{20}}\\=\sqrt[20]{ y^{7} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{4} - \frac{3}{5} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{5} - \frac{2}{3} }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)