Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{5}{4}}}\\= y^{ \frac{3}{4} - \frac{5}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{5}{2} - \frac{3}{2} }= q^{1}\\\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{2}{3} - (\frac{-2}{5}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{-1}{4}}}\\= a^{ 1 - (\frac{-1}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
6. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{6} - (\frac{-4}{5}) }= y^{\frac{29}{30}}\\=\sqrt[30]{ y^{29} }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{3}{4} - \frac{1}{5} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{4}{3} - (\frac{-5}{2}) }= q^{\frac{23}{6}}\\=\sqrt[6]{ q^{23} }=|q^{3}|.\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{4} - (\frac{-4}{5}) }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{2} - \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)