Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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