Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{4} - (\frac{-4}{3}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{5}{2}}}\\= x^{ 1 - \frac{5}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
3. \(\dfrac{y^{2}}{y^{\frac{2}{5}}}\\= y^{ 2 - \frac{2}{5} }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{5}}}{q^{2}}\\= q^{ \frac{-3}{5} - 2 }= q^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ q^{13} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{3} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{3}}\\---------------\)
6. \(\dfrac{y^{2}}{y^{\frac{5}{4}}}\\= y^{ 2 - \frac{5}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{4} - \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{6}}}\\= a^{ 1 - \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{5} - \frac{5}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{2} - (\frac{-5}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)