Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{1}{3}}}\\= q^{ -1 - \frac{1}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{2}}}{x^{1}}\\= x^{ \frac{-5}{2} - 1 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{3} - (\frac{-2}{5}) }= a^{\frac{31}{15}}\\=\sqrt[15]{ a^{31} }=a^{2}.\sqrt[15]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{2} - \frac{2}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{-2}}\\= y^{ \frac{-1}{3} - (-2) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{1}{5}}}\\= x^{ -1 - \frac{1}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
8. \(\dfrac{y^{2}}{y^{\frac{-1}{5}}}\\= y^{ 2 - (\frac{-1}{5}) }= y^{\frac{11}{5}}\\=\sqrt[5]{ y^{11} }=y^{2}.\sqrt[5]{ y }\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{3}{2}}}\\= a^{ 1 - \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-3}{4} - \frac{5}{4} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{-2}}\\= x^{ -1 - (-2) }= x^{1}\\\\---------------\)