Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{5} - (\frac{-5}{2}) }= y^{\frac{27}{10}}\\=\sqrt[10]{ y^{27} }=|y^{2}|.\sqrt[10]{ y^{7} }\\---------------\)
2. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{5} - \frac{1}{3} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{2} - (\frac{-3}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{4} - \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{2} - (\frac{-3}{5}) }= a^{\frac{31}{10}}\\=\sqrt[10]{ a^{31} }=|a^{3}|.\sqrt[10]{ a }\\---------------\)
6. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
7. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-1}{5} - \frac{3}{4} }= y^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ y^{19} }}=\frac{1}{\sqrt[20]{ y^{19} }}. \color{purple}{\frac{\sqrt[20]{ y }}{\sqrt[20]{ y }}} \\=\frac{\sqrt[20]{ y }}{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
11. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{3} - \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)