Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
2. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{3}{4} - (\frac{-1}{5}) }= x^{\frac{19}{20}}\\=\sqrt[20]{ x^{19} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{2}{3} - \frac{3}{5} }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-3}{2} - (\frac{-3}{2}) }= q^{0}\\=1\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\dfrac{q^{\frac{-5}{3}}}{q^{-1}}\\= q^{ \frac{-5}{3} - (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
8. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
10. \(\dfrac{x^{2}}{x^{\frac{1}{6}}}\\= x^{ 2 - \frac{1}{6} }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{4}{5}}}\\= y^{ 1 - \frac{4}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)