Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{4}{5} - (\frac{-5}{4}) }= a^{\frac{41}{20}}\\=\sqrt[20]{ a^{41} }=|a^{2}|.\sqrt[20]{ a }\\---------------\)
3. \(\dfrac{a^{2}}{a^{\frac{-1}{2}}}\\= a^{ 2 - (\frac{-1}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-3}{5} - (\frac{-4}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{4} - (\frac{-2}{3}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{2} - \frac{5}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{4} - \frac{1}{3} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{1}{3}}}\\= a^{ -1 - \frac{1}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{5} - \frac{2}{3} }= a^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ a^{13} }}=\frac{1}{\sqrt[15]{ a^{13} }}. \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)