Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{4}{5}}}\\= q^{ -2 - \frac{4}{5} }= q^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ q^{14} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{2} - (\frac{-5}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{5}{3}}}\\= x^{ -1 - \frac{5}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{5}{3} - (\frac{-2}{5}) }= x^{\frac{31}{15}}\\=\sqrt[15]{ x^{31} }=x^{2}.\sqrt[15]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-4}{5} - (\frac{-3}{4}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{6} - \frac{2}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{3} - (\frac{-4}{5}) }= q^{\frac{17}{15}}\\=\sqrt[15]{ q^{17} }=q.\sqrt[15]{ q^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{2} - (\frac{-1}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{y^{\frac{-4}{3}}}{y^{1}}\\= y^{ \frac{-4}{3} - 1 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)