Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{5} - (\frac{-2}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-3}{4} - \frac{1}{5} }= a^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ a^{19} }}=\frac{1}{\sqrt[20]{ a^{19} }}. \color{purple}{\frac{\sqrt[20]{ a }}{\sqrt[20]{ a }}} \\=\frac{\sqrt[20]{ a }}{|a|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{3} - (\frac{-5}{2}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{6}) }= x^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ x^{13} }}=\frac{1}{\sqrt[30]{ x^{13} }}. \color{purple}{\frac{\sqrt[30]{ x^{17} }}{\sqrt[30]{ x^{17} }}} \\=\frac{\sqrt[30]{ x^{17} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{4} - (\frac{-1}{3}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{5} - \frac{1}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{3}}}{q^{1}}\\= q^{ \frac{-5}{3} - 1 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-2}{3}) }= y^{0}\\=1\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{2} - \frac{1}{3} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)