Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{4} - \frac{1}{4} }= y^{0}\\=1\\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{4}{5} - \frac{5}{2} }= a^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{7} }}=\frac{1}{|a|.\sqrt[10]{ a^{7} }} \color{purple}{\frac{\sqrt[10]{ a^{3} }}{\sqrt[10]{ a^{3} }}} \\=\frac{\sqrt[10]{ a^{3} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{1}{4}}}\\= x^{ 1 - \frac{1}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
4. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-1}{2} - \frac{3}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{3}{5} - (\frac{-2}{3}) }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-3}{5} - (\frac{-3}{4}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{3}{2} - (\frac{-1}{5}) }= y^{\frac{17}{10}}\\=\sqrt[10]{ y^{17} }=|y|.\sqrt[10]{ y^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{4}{3} - (\frac{-4}{5}) }= y^{\frac{32}{15}}\\=\sqrt[15]{ y^{32} }=y^{2}.\sqrt[15]{ y^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{2} - (\frac{-4}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)