Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-5}{2}) }= y^{\frac{23}{10}}\\=\sqrt[10]{ y^{23} }=|y^{2}|.\sqrt[10]{ y^{3} }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
3. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
4. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{6}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{6} - (\frac{-2}{5}) }= a^{\frac{37}{30}}\\=\sqrt[30]{ a^{37} }=|a|.\sqrt[30]{ a^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{-2}}\\= y^{ \frac{1}{3} - (-2) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{5}{3}}}\\= x^{ -1 - \frac{5}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-5}{3}}}\\= q^{ -1 - (\frac{-5}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)